Good points, CharlotteBMM. Rodney Dangerfield was always given that freedom, in his films. Let's say when he was hired to do a part, he was hired strictly to be him. So in a way, he didn't play a character, he played Rodney Dangerfield. Of course, that was a match made in heaven (and the directors were really looking for a character just like Rodnet, there), so it came off funny. It's just that he never really got to act in movies where it called for someone else, outside of his known comedy routines.
Rick Moranis is one of those guys that had a bit of both. Certain movies he was able to be himself and adlib a bunch. (Case in point. Spaceballs, in which a large percentage of Dark Helmut's entire on-screen presence was written on-the-fly by Rick Moranis. Mel Brooks mentioned it several times, in the director's commentary soundtrack, of the Spaceballs DVD. Then, of course, you have Rick Moranis' early movies, where he was also free to do his stuff. "Strange Brew" etc.)
And then he was in movies in which he was asked to play a character and, in general, that character wasn't meant to be funny. In those, he played a rather straight man character who simply had a quirky occupation or scenario happen to him. (Case in point. The Honey I shrunk the Kids movies, among other things.) In those cases, it was as if Rick was asked to play second fiddle to whatever comedy 'They' wanted to serve.
And don't forget Rick Moranis is also Candian. Rick and John Candy both got their big start on a Candian Night comedy show called "Second City TV". It was basically, the Candian Saturday Night Live.