Sharon and Chris are separate people

[dcfan01]

Spoiler:

Yukiko confronted Vermouth and it was clear that Chris/Sharon were the same

Now that you mention it, it is strange that she allowed so many people be alive after discovering her true identity..
Apart from the case you mentioned, she knows that conan and jodie know that secret too.
I can understand why she didn't kill conan, but Jodie?
She past right by her when checking if Akai was really dead, and yet, she didn't kill her.
There are 4(3) people in Japan that know her real identity(That she knows of: Conan, Haibara, Jodie and Akai), if she was really trying to hide it from the BO, I think she wouldn't take so many chances..

[Chekhov MacGuffin]

Now that you mention it, it is strange that she allowed so many people be alive after discovering her true identity..
Apart from the case you mentioned, she knows that conan and jodie know that secret too.
I can understand why she didn't kill conan, but Jodie?
She past right by her when checking if Akai was really dead, and yet, she didn't kill her.
There are 4(3) people in Japan that know her real identity(That she knows of: Conan, Haibara, Jodie and Akai), if she was really trying to hide it from the BO, I think she wouldn't take so many chances..

It's hard to off people in public without prep. Also murdering an FBI agent (Jodie told the MPD) in front of a police station seems like a poor plan - it would be the perfect excuse to get even more FBI involved in Japan, legally this time. The Japanese Police would likely get involved too because random hits on FBI are a bit suspicious. If Jodie is going to die, it has to be done in a clever way that doesn't give the rest of the FBI excuses to come check it out. Besides, killing Jodie won't solve the fundamental problem if Vermouth's secret is on record in the FBI somewhere. We know Daddy Starling kept records on Vermouth, so why would his daughter not?
Even worse Vermouth has her hands tied, that showdown with Jodie never happened according to the story she told the BO. If someone in the Org hears about Jodie dying and traces the killing to Vermouth, it might lead to some awkward motive questions.
Honestly though, I think real reason is because having Vermouth kill Jodie would be inconvenient to Gosho for plot purposes.

Besides, the main problem may not be Vermouth's multiple identity secret so to speak, but hiding how her secret came to be: i.e. the freaky science behind it. Prioritizing Haibara for death makes sense in this context because Haibara would be the first to understand.
Imagine a scenario where, say, both Vermouth and the boss of the Black Org were affected by an unrepeatable science experiment gone weird, and the boss has his/her name connected with that project because this was before the days of the Org and all its secrets. If someone tied Vermouth to the program, they could possibly trace it back to the boss. This is just a hypothetical scenario, but I think it is a good example to show the sort of situation that might give rise to different priorities of secrecy within Vermouth's secrets.

[Akai Shuuichi]

There are 4(3) people in Japan that know her real identity

Add to that Yukiko and probably a lot of other FBI agents. If Vermouth had a chance she would finish Jodie off not because she knows her identity as much as because she's a nuisance to the Org. She couldn't kill her in front of the police HQ(as Chek said). And she would've killed her in the confrontation if it wasn't for Akai. She probably kept Yukiko alive for the sake of their friendship and since she's "Angel's" mother.

[Citan]

"Angel" is Ran. If Yukiko is Ran's mother than she and Kogoro have some explaining to do. I think you mean that she is "Cool Guy's" (Shinichi's) mother.

I've spent alot of time thinking about the mysteriousness surrounding Sharon/Chris/Vermouth, and I have thought of only one way for them to be different people and still look the same and have the same fingerprints. What if... Chris is a clone of Sharon? I know there's no evidence the BO is involved in cloning but they do seem to be trying to find a means of immortality, or at the very least reverse the aging process. If Sharon wasn't de-aged by some kind of drug then cloning is the only other way I can think for her to suddenly appear as her younger self fingerprints and all.

[Yottas]

I have thought of only one way for them to be different people and still look the same and have the same fingerprints. What if... Chris is a clone of Sharon?

I don't think so...
A better explanation would be that Chris and Sharon are twins, but Chris isn't aging...

Yottas

[Chekhov MacGuffin]

I have thought of only one way for them to be different people and still look the same and have the same fingerprints. What if... Chris is a clone of Sharon?

I don't think so...
A better explanation would be that Chris and Sharon are twins, but Chris isn't aging...

Yottas

Neither clones nor identical twins have matching fingerprints. Fingerprint patterns are randomly determined during development, same with iris patterns.

[Akai Shuuichi]

"Angel" is Ran. If Yukiko is Ran's mother than she and Kogoro have some explaining to do. I think you mean that she is "Cool Guy's" (Shinichi's) mother.

Yeah my bad.

[Citan]

I have thought of only one way for them to be different people and still look the same and have the same fingerprints. What if... Chris is a clone of Sharon?

I don't think so...
A better explanation would be that Chris and Sharon are twins, but Chris isn't aging...

Yottas

Neither clones nor identical twins have matching fingerprints. Fingerprint patterns are randomly determined during development, same with iris patterns.

Ah, well that kills that idea then. Thanks for the info Chekhov. I guess that leaves us with the "Vermouth took an APTX-like precursor drug which stopped her aging" theory. My problem with that is APTX itself is extremely dangerous and unlikely to get the result you want. The drug she took had to be a precursor to it probably made by Haibara's parents. That drug would have been even more dangerous and unpredictable than APTX so why would Vermouth agree to take it? Did Haibara's parents have a more complete drug? If so what happened to THAT research? Was it destroyed when they died forcing Haibara to have to start over with the APTX? If so who destroyed it? The Organization wouldn't have done it as it would have jeopardized the project. One can only assume the Miyanos destroyed it intentionally hoping to derail the project. Perhaps that was what led to their deaths? I"m getting off topic here. My point is I couldn't see Vermouth willingly taking APTX let alone a less complete precursor drug unless she was reasonably sure it would work.

[Elixir]

^There's still no explanation given in the manga about Vermouth's non-aging. So speculating about a 'speculation' will be more complicated. But following your line of thought,

My point is I couldn't see Vermouth willingly taking APTX let alone a less complete precursor drug
unless she was reasonably sure it
would work.

there could be a lot of reasons:
a. She tried to commit suicide, like Haibara
b. She was forced to take it, like Shin'ichi
c. She mistook it for a medicine, lolz

That would assume that Vermouth's non aging is due to APTX. It is also possible she is not connected to it , or she is the inspiration of the study.

[Akai Shuuichi]

I highly suspect that. Why did APTX work differently than on Haibara and Conan, I mean she's not a kid after all, maybe there was a more 'complete' drug that only few knew about.

[Conan-chandesune]

I highly suspect that. Why did APTX work differently than on Haibara and Conan, I mean she's not a kid after all, maybe there was a more 'complete' drug that only few knew about.

That would mean APTX is the Super Solider Serum of Conan's universe which got lost. Mind you, it fits the "over a decade" description.

[dcfan01]

Just to make things more clear, I made a timeline of everything I could think is related to Vermouth:

Spoiler: Timeline

EDIT: added references: in green the facts, in orange the conjectures.
CT=Current Timeline

30 years ago:
-Souhei Dejima borrowed Atsushi Miyano's inherited house.
That was the last time he saw him. (ch 423)

25+ years ago:
-Atsushi Miyano meets Elena Miyano (since 20 years prior to CT they have a 5 y/o daughter. ch423)

20+ years ago:
Jodie's Father, an FBI agent was investigating Vermouth and kept a secret file about her.
(These are Jodie's words ch433)

20 years ago:
-Vermouth kills Jodie's father ch433
-Her face from back then is the same as now ch433 (Yet Chris was suppoused to be 9 y/o, since she is 29 in CT ch239)
-Jodie was 7-8 y/o (since she is 28 in CT ch270)
-Jodie keeps her father's glasses with Vermouth fingerprints ch433
-Yukiko was 17 (Since she is 27 in CT source:Conan Drill)
-Atsushi and Elena Miyano were married and had a 5 y/o daughter (Akemi) (ch 423)
Around 20 years ago:
-Yukiko starts her carreer as an acrtress, while still being in high school ch414
-Sharon and Yukiko studied disguising techniques together, under the tutelage of Toichi Kuroba ch351
-It is a safe assumption that Sharon was 29 and started using aging makeup from here on.
-They became close friends ch351

18 years ago:
-Birth of Shijo since she is 18 in CT (source:conan drill)
-Shijo's parents are developing the Silver Bullet experiment
-Elena Miyano taped some words for shijo to hear and gave the tapes to Akemi(7)

11+ years ago:
Sharon said to Yukiko that she stopped seeing her daughter 10 years ago (that is in the golden apple case 1 year prior to CT ch351)
Everything in this timeframe is from when she still met with Chris
-Sharon had a made up husband and a daughter (ch 351)
-Sharon won an Oscar (ch 351)
-Sharon's husband died (ch 351)
-Sharon said to yukiko she taught Chris(<18) how to disguise (ch 351)

Around 11 years ago:
-Sharon stopped seeing Chris (ch 351)

10 years ago:
-Yukiko(27) meets with kuroba toichi, her former disguising mentor ch573

8 years ago:
-death of Toichi Kuroba ch156

5 years ago:
-Akai infiltrates the BO ch599
-Sherry was already working as a high ranked scientist for the BO ch599

2+ years ago:
-Sharon had a quarrel with Itakura Suguru on a filmset, and since then they aren't in good terms ch823
Yukiko's information is based on rumors and she doesn't give a time reference, but she said that Sharon had to change her voice over the phone, what implies that she was already on bad terms

2 years ago:
-Akai is given the codename Rye and is called to meet Gin, and at the same time, is discovered by the BO ch599
-Tequila shows up at the office of computer graphics designer/games system engineer Itakura Suguru to say
he was interested in the particular “system program” Itakura stopped developing one year ago. ch380

1 year ago:
-Sharon invites Yukiko and Shinichi to her new show "Golden Apple" in NY. ch350
-Vermouth disguises as a serial killer in order to lure Akai out, but fails to kill him
instead, she is saved by Shinichi and Ran. ch354
-Suguru Itakura is given a forced one year deadline to finish the program Tequila was interested in one year ago. ch380.

Less than 1 year ago:
-Sharon dies and Chris appears in public for the first time. ch344
-Yukiko attends the funeral ch344.
-Jodie also attends, and starts suspecting Chris after seeing her for the first time. ch433
-Jodie compares Chris' fingerprints with sharon's and they match perfectly, together with those vermouth left in her father's glasses ch433

Current timeline:
-Vermouth admits to Yukiko that "It's actually quite tough, pretending that it's not just your face, but everything about you that's aging too" ch823
-Haibara finds 4 tapes her mother gave to akemi with messages for her birthdays 1 to 20 ch425

First of all we can deduce that since the tapes contained messages for Shijo's years 1 to 20, Elena should have recorded them while Shijo was < 1, probably while she was pregnant. She knew by that time that she would have to leave Akemi and Shijo, and therefore taped those messages.
This means that the messages are 18 years old, and so is the Silver Bullet project. By that time, Vermouth's aging had already stopped..

What is difficult to know is if Vermouth's aging goes on par with Sharon's and then stops, or if her aging stopped before Sharon, and Sharon is just another personality she created..
I'm inclined to think that Vermouth was Sharon until the age of 29(most likely 20 years ago), when (for some reason) she stopped aging.
This event might have been related to Jodie's father investigation, leaving her no choice but to kill him while that investigation was still secret.
It is also 20 years ago that Atsushi Miyano had a serious matter to discuss with Souhei Degima his (only?) friend; so serious that he stayed overnight with his family waiting for him.

Having stopped aging, Vermouth realised that she would eventualy need a way to look older, thus started learning disguise techniques from Kuroba Toichi.
For some reason she also needed a family, so she created it. She kept talking to everyone she knew as Sharon about her husband and daughter (At one point she told Yukiko how her daughter begged her for some disguising lessons). Everything was fine, until at some point, 9 years after that (almost 11 years before current timeline) she started to tell people that her husband died, and that she doesn't consider Chris her daughter anymore.
All we know is that before that she won an Oscar, but even if that might have raised interest in her family, she was already a well known actress, so I think there has to be other reason for this development.

The last story we know about Sharon is that she had a clash with Suguru Itakura in a film set, then her intervention in the NY case and finally, her death lees than a year ago.
Once again, a family member is killed without reason.. you could argue that it would allow Chris to show herself without makeup, and sice Chris and Sharon can't appear anywhere together, it was convinient to "kill" her, BUT, given Vermouth disguising skills, it wouldn't be impossible to disguise someone as Sharon and show Chris together with her..
Also, "Kill" a very famous person just for the convinience of not wearing makeup? I don't think so..
There has to be another reason, just like before..

What I expect from the next BO arc is some kind of story that binds together these 3 holes in Vermouth's life:
20 years ago, when she (probably) stopped aging
11 years ago, when she "killed" her husband and separated Sharon from Chris and
1 year ago, when she "killed" Sharon and made Chris a public figure.
together with the silver bullet experiment and Jodie's father investigation.

[Chekhov MacGuffin]

Just to make things more clear, I made a timeline of everything I could think is related to Vermouth:...

I wanted to let you know I am formulating a response about some of the specific timeframes you mentioned but it is taking a while because I have to do some research and I'm out of town.

[dcfan01]

Just to make things more clear, I made a timeline of everything I could think is related to Vermouth:...

I wanted to let you know I am formulating a response about some of the specific timeframes you mentioned but it is taking a while because I have to do some research and I'm out of town.

looking forward to it.
Also, when I have more time, I'll add some references to make research easier.. It should also help differentiate between conjectures and fact-based items on the list.

[Citan]

I know this question is pretty well settled, but after having more time to think I realize we have more proof that Sharon and Chris are definitely one and the same than merely the FBI's fingerprint analysis.

Way way back many moons ago we were shown a scene in which Gin and Vodka were waiting in a Jazz Bar and were eventually approached by a waiter that turns out to be Vermouth. Gin scolds Vermouth for this stating his concern that someone might notice the "Famous Actress Chris Vinyard" working as a waiter in a Jazz Bar which would lead to awkward questions.

This scene confirms Vermouth's current public persona is Chris Vinyard, and yet during her confrontation with Conan and the FBI she both recognizes Jodie as the little girl from 20 years ago, and also remembers Ran saving her life while she was disguised as the "Silver Haired Man" in New York. Her severe emotional response to Ran's actions during that incident precludes any possibility of her being simply told about that incident after the fact. Not even she is that good an actress.

So basically what this proves is that the current Vermouth, confirmed by Gin himself to be Chris Vinyard, is the same Vermouth met by both Ran in New York AND Jodie 20 years ago in her family home. The only way for this current Vermouth to have been at both sites. The only way she could remember both missions, is for Sharon and Chris to be the same person.