Okay, here’s an odd phenomenon. In some film series (or just a film and its sequel), they will have mostly the same principal actors, it’s in the same continuum, but there’s an actor or actress in two different installments playing a different character. Here are some obvious examples, give me some better ones:
Stan Lee, who plays slightly different characters in most of the Marvel Comics movies. In Captain America: The First Avenger, he’s a general, but in Winter Soldier he’s a Smithsonian rent-a-cop.
Sofia Coppola plays the infant Michael being baptized in The Godfather. In Part Two she’s an immigrant kid on a boat. In Part Three she’s Mary Corleone, one of the primaries.
Maud Adams has been in three James Bond movies, all starring Roger Moore: She’s Andrea, the beta Bond Girl in The Man with the Golden Gun; Octopussy in Octopussy; and she has an uncredited bit part in A View to a Kill.
I’m excluding TV shows, although there’s a proud tradition of this on the small screen as well.
There are a lot of these in the James Bond series. Maud Adams has already been mentioned. There’s also:
Charles Gray – “Mr. Henderson” in You Only Live Twice, he came back to play Ernst Stavro Blofeld, the head of S.P.E,C,T,R,E., in Diamonds are Forever
Ed Bishop was Hawaii Capcom in You Only Live Twice] and Klaus Hergeshimer in Diamonds are Forever
Joe Don Baker was Brads Wittaker, the chief Bad Guy, in The Living Daylights, but came back to play CIA agent Jack Wade in * Goldeneye* and Tomorrow Never Dies.
Walter Gotell was SPECTRE agent Merzeny in From Russia With Love, but came to play General Gogol in a bunch of sequential movies – every one from The Spy Who Loved Me77) to The Living Daylights (1987) Martine Beswick was Vida in From Russia with Love and Paula Kaplan in Thunderball.
There are others, mostly in really mnor roles, like Ed Bishop.
Another one - the first I thought of - Bruce Spence. He was the Gyro Captain in Mad Max 2, and Jedediah the Pilot in Mad Max Beyond Thunderdome. Similar characters, granted, but different.
Hunh. Looking up those links, I see Bruce was in Revenge of the Sith. Played the pale guy Obi Wan talked to on that planet where Obi killed Grievous. #I did not know that.
Bruce Spence played the Gyro Captain in The Road Warrior and Jedediah in Mad Max beyond Thunderdome. Hugh Keays-Byrne played Toecutter in Mad Max and Immortan Joe in Mad Max: Fury Road. Max Fairchild played Benno Swaisey in Mad Max and the Broken Victim in The Road Warrior.
Speaking of Mad Max - the villain Toecutter from the original Mad Max played the villain Immortan Joe in Mad Max: Fury Road.
Warwick Davis played a few different characters in Return of the Jedi, Phantom Menace, and Force Awakens.
Pat Roach played the airplane mechanic who got chopped up in Raiders of the Lost Ark, the head guard that got chopped up in Temple of Doom, and a gestapo officer in Last Crusade. I don’t think he got chopped up in the last one.
Amy Yasbeck played John Ritter’s shrew of a wife in Problem Child, then his much nicer new love interest in Problem Child 2. They were also married in real life, if you didn’t know, and while it’s outside of the scope of this topic, they also played a married, expecting couple on an episode of the Cosby Show.
If you consider the Marx Brothers film a series, there’s Margaret Dumont. Also Walter Woolf King, who played the bad guy in A Night at the Opera and Go West and Sig Ruman in A Day at the Races and A Night in Casablanca.
Ruman also played two different villains in the first two Mr. Moto movies. Leon Ames also played two different characters in two different movies in that series, too.
Turhan Bey played Manuel Retana in The Gay Falcon* and Jules Amthor in The Falcon Takes Over
The Three Stooges always ran up against Vernon Dent or Bud Jamison, playing different characters.
*No, he wasn’t like that. “Gay” was the Falcon’s first name.
Bela Lugosi played Bad Guy Roxor in *Chandu the Magician * (1932), but played Chandu himself in The REturn of Chandu (1934)
Lugosi, of course, famously played several characters in the linked Universal Monster Movies of the 1930s and 40s. He was Dracula in Dracula and Abbott and Costello Meet Frankenstein, Ygor in Son of Frankenstein and Ghopst of Frankenstein, and played the Frankenstein Monster himself in Frankenstein Meets the Wolfman.
Lon Chaney, Jr. should have gotten an award for playing just about every part. He was Lawrwnce Talbot, the Wolfman in The Wolfman, Frankenstein Meets the Wolfman, House of Frankenstein, House of Dracula, and Abbott and Costello Meet Franmkenstein. But he was also Counmt Alucard, The Son of Dracula. He was Kharis the Mummy in The Mummy’s Tomb, The Mummy’s Ghost, and The Mummy’s Curse[. He was The FRanklenstein Monster in The Ghost of Frankenstein and in a few uncredited scenes in Abbott and Costello Meet Frankenstein.
**Edward Van Sloan ** was Van Helsing in Dracula and Dracula’s Daughter, and also Professor Waldmann in *Frankenstein * and Doctor Waller in The Mummy
Boris Karloff was the Frankenstein Monster in Frankenstein, Bride of Frankenstein, and Son of Frankenstein, then swore off the role, but he came back as the Mad Doctor Gustav Niemann in House of Frankenmstein
And, of course, Dwight Frye was *Renfield in Dracula, Fritz in Frankenstein, and Karl in Bride of Frankenstein.(He may also have played villagers in Son of Frankenstein and Ghost of Frankenstein)
Many of them played identical or similar roles for other film companies or on TV, but these are the ones in the connected series of Universal films.
Consider the Universal horror series of the 30s and 40s.
Lionel Atwill made his first series appearance in Son of Frankenstein. He subsequently appeared in every Frankenstein film in the series–Ghost of Frankenstein, Frankenstein Meets the Wolf Man, House of Frankenstein, and House of Dracula. He played a different character in each film. And these were films that were, in many cases, released only a year apart.
Patric Knowles appeared as a gamekeeper in The Wolf Man. Two years later, he showed up in Frankenstein Meets the Wolf Man, playing a doctor.
Evelyn Ankers appeared in several different Universal horror films, including The Wolf Man, The Ghost of Frankenstein, Son of Dracula, as well as many others, playing a different character each time.
And lastly, Lon Chaney, Jr. managed to play just about every monster there was, from The Wolf Man to the Frankenstein Monster to Dracula to the Mummy.
Lawrence Makoare played Lurtz in Lord of the Rings: The Fellowship of the Ring, Gothmog and the Witch-King in Lord of the Rings: The Return of the King, and orc commander Bolg in The Hobbit: The Desolation of Smaug.
A couple of the actors from Return of the Living Dead who got killed in that movie returned in Return of the Living Dead II as new characters. They even lampshaded the re-appears (“Do you have the feeling something like this happened to us before?”) – James Karen and Thom Mathews. Neither returned for any further sequels, although James Karen and Don Calfa, (who only appeared in the first one) were offered parts in Return of the Living Dead III.
Bruce Spence was also in The Matrix Reloaded and Return of the King. I believe he’s the only actor who was in all three of the big SF/fantasy franchises of the early 2000s.
(Yeah, I realize the OP asked for “same film series,” but I think this is an interesting bit of trivia nevertheless.)
I’ll throw in Bruce Campbell in for the Sam Raimi Spider-Man films. I guess there’s nothing that proves he isn’t the same character in each film, and I remember some fans convinced he was actually Mysterio, but I’m counting because by god you took the James Bond ones from me.