Going back to James Stewart, when I think of him in The Philadelphia Story and then in Vertigo, or in The Glen Miller Story, I do see those characters as completely different.
This may have something to do with the fact that I don't watch television and have never seen the man 'being himself'.
I don't see an actor as a 'celebrity' I see them as workers doing part of a job - same as a director or cameraman.
For me, Stewart was totally convincing. Whatever part he took on, he seemed to have a genuine understanding of that character.
If anything, I think he was under-rated.
The Philadelphia Story with Cary Grant and Katherine Hepburn. 1940