Generally, when a movie or TV show has to replace a prominent cast member, they try to cast someone who loks at least approximately the same.
When Richard Harris died, they needed a new Dumbledore. Michael Gambon didn’t look significantly different – we still got an old white guy with a long white/grey beard.
when Roddy MacDowell didn’t appear as Cornelius in Beneath the Planet of the Apes, his replacement, David Watson, didn’t look all that different (well, who wouldm, under the ape makeup). In penance, MacDowell had to play Cornelius in all the other Planet of the Apes movies in that first series, and on the TV show besides.
Dick Sargent isn’t a dead ringer for the Dick York he replaced in Bewitched, but they’re not radically different.
But some TV shows or movie series Just Don’t Care. The chief offender in this regard is arguably the James Bond franchise.
after years of teasing us by not showing us the face of Ernst Stavro Blofeld (Spectre #1), whose face was coyly hidden while he stroked that damned white cat, they finally decided to show us in You Only Live Twice. They tried out actor Jan Werich, but the bearded man looked to the director like “a poor, benevolent Santa Claus”, not the menacing Evil Villain the previous films hinted at. So they replaced him with a bald Donald Pleasance, with a nasty scar down the side of his face and around one eye. His voice didn’t have the deep menace of the previous films, and he was shorter than Connery, so he didn’t really look all that imposingly evil, either. For the next film , On Her Majesty’s Secret Service, they got Telly Savalas, who was, at least, bald, but appeared significantly taller, and who was (a plot point) missing part of his earlobes. But there was no face scar. Following this, they got Charles Gray to play him in Diamonds are Forever. This was a confusing choice. Gray had no scars, all his earlobes, and all his hair. He had also played Agent Henderson in You Only Live Twice, looking exactly the same. They skimped on the ending which was supposed to feature a sub chase, so we’re never quite sure what happened to him. They wanted to have Blofeld as the villain in The Spy Who Loved Me, but they lost the rights to the character in a legal dispute, so they substituted Stromberg who was Blofeld in All but Name. Curt Jurgens played him, still white-haired and scarless, but now with a Germanic accent. At the opening of For Your Eyues Only an unnamed bald villain in a wheelchair threatens Bond with a remote-controlled helicopter. We never see his face, but he’s still petting that damned white cat. He’s clearly supposed to be Blofeld, even though they couldn’t use the name. I’s tempting to think he was crippled in that sub accident at the end of Diamonds are Forever, which explains the chair. But he’s bald, like Donald Pleasance/Telly Savalas Blofeld. Maybe Charles Grey Blofeld lost his hair in the accident, too. The company that made Never Say Never Again, who got the rights to Blofeld, significantly got someone who looked completely different – Max von sydow, with his brown hair. They gave him a cat to pet, too (Blofeld didn’t have such a familiar in Fleming’s books), but his cat is orange. Finally, in S.P.E.C.T.R.E. they got Christoph Waltz to play Blofeld as a guy who looked like – Christoph Waltz, with hair and no scars and everything. Although by the time the film ends he’s had an accident that gives him a facial scar kinda like Donald Pleasance’s, which brings it all full circle, or something. I find it significant that when Mike Myers created his Dr. Evil character for the Austin Powers movies, he patterned him after Donald Pleasance Blofeld, bald head, scar, and all.
The Bond franchise also gave us the Magical Changing Felix Leiter. We had Jack Lord as McGarrett Leiter in Dr. No, Cec Linder as white-haired balding Leiter in Goldfinger, rik van Nutter as Surfer Boy Leiter in Thunderball, Norman Burton as forgettable-second-banana Leiter in Diamonds are Forever, David Hedison as The Fly/Captain Crane Leiter in Live and Let Die and again (the first to reprise the role) in License to Kill, John Terry as Second Surfer Boy Leiter in the Living Daylights. Never Say Never Again gave us Bernie Casey as The First Black Leiter (Connery supposed suggested the race change because it might make the role more memorable), and Eon followed up with Jeffrey Wright as The Second Black Leiter and the Second Guy to Play Leiter Twice in Casino Royale and Quantum of Solace. (There was also Michael Pate as the British “Clarence Leiter” in the 1954 TV Casino Royale)
Of course, Bond himself was played by a slew of actors who varied quite a bit – Sean Connery, George Lazenby, Roger Moore, Timothy Dalton, Peirce Brosnan, Daniel Craig (and Barry Nelson as “Jimmy Bond” in he TV Casino Royale, along with David Niven and a slew of others in the 1967 Casino Royale)
I was started thinking along these lines when I watched The Magnificent Seven and its sequels. Yul Brynner played lead gunslinger Chris Adam (who’s supposed to be Cajun – Brynner was Hollywood’s main go-to ethnic) in the original film and its first sequel, the only actor of the Seven to return from the first film. Robert Fuller replaced Steve McQueen and Julian Mateos replaced Horst Bucholz for *Return of the Magnificent Seven, although they don’t really look like the original actors. (But they’re not radically different, except that Mateos looks more Hispanic than Bucholz, which is appropriate). But for the next two sequels Brynner was replaced by the non-bald George Kennedy and Lee van Clef. I guess they figured van Cleef had been in Sergio Leone westerns, so they’re interchangeable.
And don’t get me started on Sting II. Chubby Jackie Gleason and Full Head of Hair Mac Davis replacing Paul Newman and Robert Redford? Oliver Reed in place of Robert Shaw? And the names aren’t the same, but the situations are, so it’s like a parallel-universe version?
What else you got?