We've got examples from each variance, thanks to 'The West Wing' which (as everybody should know by now) had to get its own TV dimension because of its different line of Presidential succession after Nixon.
The first one we've brought up in the past: Josiah Bartlet - President in the "West Wing Dimension", Boston Doctor in Earth Prime-Time. Instead of getting a doctorate in economics, Bartlet practiced medicine, as seen in 'St. Elsewhere'.
However, there must have been a slight shift in the circumstances of his conception, so that a different sperm fertilized his mother's egg.
The other example never actually appeared on 'The West Wing' - Henry Landingham, husband of the President's secretary Dolores Landingham. (She may have already been a widow when we met her at the Oval Office on the show.)
Back in 1965 on the timeline for the main Toobworld, an FBI agent named Landingham was conducting a background check on advertising executive Don Draper for the Department of Defense (as seen in last week's 'Mad Men'.) There was no mention of his first name, so it could have been Henry; and his personal life was never an issue, so he could have had a wife named Dolores and twin sons named Andrew and Simon who died in Viet Nam... just as it was for his doppleganger back in the "West Wing Dimension".
Like Muskie the Muskrat would say, "It's pozz'ble, it's pozz'ble...."
It's tempting to toss 'Mad Men' over to 'The West Wing' world entirely because of all its Zonks (because they show scenes from actual TV series and identifying them). Those other TV shows should be sharing the same world as 'Mad Men'. But I've made peace with that type of discrepancy and have adapted Andy Warhol's credo for it: In Toobworld, just about anybody can have a TV show made about them. So despite all its faults the two Landinghams can't be one and the same.