Again, I think we're mostly talking typecasting here, not actual instances of the actors playing the same character under a different name. I don't think every cop played by Clint Eastwood is really the same guy . . . .
On other hand, most of the classic movie comics did just play the same character in different situations. The Marx Brothers, Abbot & Costello, Martin & Lewis, etc. Almost makes you wonder why the screenwriters bothered to name their characters "Chip" or "Don Lewis" or whatever. Aside from some of Groucho's more colorful aliases (Cap'n Spaulding, Rufus T. Firefly, etc), there was really no point. Does anybody actually remember the names of the characters played by Harpo or Chico? Harpo was always Harpo: with the same costume, make-up, and schticks.
Ditto for Abbott and Costello. Even the titles of the films referred to the actors, not the characters they were supposedly playing. "Abbott & Costello Meet Frankenstein," "Abbott and Costello Meet Captain Kidd," etc. They played the same characters in every movie, just in different locations and eras.