Airplane! and Zero Hour. 
Not quite the same thing, but the strange case of Exorcist: The Beginning and Dominion: A Prequel to The Exorcist might count.
Paul Schrader had wrapped production on The Beginning and was working on editing and effects when the studio decided they didn’t like what he’d come up with, fired him, and brought in Renny Harlin to finish the movie. Harlin recast several characters, reshot several scenes, and changed the ending, but ended up keeping much of Schrader’s footage in the released version. Schrader eventually got the OK to release his cut of the movie the following year under the Dominion title - resulting in two movies with mostly the same screenplay, most of the same cast, and most of the same footage, but with majorly different plot points and wildly different climaxes.
I’d like to see the Spanish version someday. I recall the things you mentioned being discussed, Lugosi’s counterpart didn’t perform well, but the Spanish version director was supposed to have been superior to Browning.
It’s included as an extra on some DVDs of the Lugosi version.
Did the Chris Rock Death at a Funeral use the same basic script as the British version? I know both had the same plot, same jokes, same potty scene, and even had Peter Dinklage as the unexpected attendee who disrupts the funeral.
I just watched the trailers of the two Death at a Funeral versions. Clearly there are some different lines. The plot is pretty close though.
Of course this is the whole point of live theatre. You can see three different versions of Streetcar Named Desire (for example), each using the exact same script and all done capably, and one will seem a tragedy, one a dark comedy, and the other a tragicomedy.
The first episode of the American office is not the same script. It is very similar and has many of the same plot points, but it is a new script. I guess you could say it used the same treatment.
The 1992 version of The Last of the Mohicans was based on the screenplay for the 1936 version of the story, but there were changes, so not exactly the same.
I’d say there were some changes. :rolleyes: The climactic scene in the '34 version is the mother of the kidnapped child – a champion biathlon competitor – grabbing a police sniper’s rifle and killing the criminal pursuing her daughter across the rooftops. Doris Day singing “Que Sera Sera” it ain’t. 
This reminded me of Betty’s audition in Mulholland Drive. We see her perform it twice with exactly* the same lines, once rehearsing, and once in the actual audition. The audition script, in full, is as follows:
Her: You’re still here?
Him: I came back. I thought that’s what you wanted.
Her: Nobody wants you here!
Him: Really?
Her: My parents are right upstairs! They think you’ve left.
Him: So… surprise…
Her: I can call them… I can call my dad…
Him: But you won’t…
Her: If you’re trying to blackmail me… it’s not going to work. You’re playing a dangerous game here. *[This is the only line that changes. In the audition, she starts with the “You’re playing…” line and then follows with “If you’re trying…”]
Him: You know what I want… it’s not that difficult.
Her: Get out! Get out before I call my dad… he trusts you… you’re his best friend. This will be the end of everything.
Him: What about you? What will your dad think about you?
Her: Stop! Just stop! That’s what you said from the beginning. If I tell what happened… they’ll arrest you and put you in jail. So get out of here before…
Him: Before what?
Her: Before I kill you.
Him: Then they’d put you in jail.
Her: I hate you… I hate us both!
But even though the dialogue is nearly identical, she performs it in two very different ways. Here’s the rehearsal, and here’s the audition. It would be awesome to see two entire movies with the same dialogue but with such different plots and meanings.
The first two Dalek stories in Doctor Who on TV were remade as movies. Mostly the same script, other than the first few minutes. But the original TV version feels darker, and the movies lighter. The way the Doctor is played is very different, too.
A recent version of this was The Lorax. Danny DeVito learned the script phonetically for the Spanish, Italian, German, and Russian language versions of the movie.
Trey Parker and Matt Stone considered doing a shot-for-shot remake of the movie The Day After Tomorrow using puppets before coming up with Team America: World Police.
The Prisoner of Zenda.
1937, black-and-white, starring Ronald Colman.
1952, color, starring Stewart Granger.
A few minor differences in staging, but the plot and dialog are nearly identical.
Originally a novel, then a stage play. I think the movie script follows the stage script fairly closely.
I have not seen the silent version of Beau Geste, starring Ronald Colman, but I have heard that the Gary Cooper version is a near shot-for-shot remake.
I think this was fairly common back in the 1940s and 1950s. The studio would re-shoot and old silent script with sound, or re-shoot and old black-and-white script in color. No sense in paying a writer to tinker with something that had already made money the first time around. 
This is somewhat common when a film is adapted from a stage play. For example, the Bela Lugosi Dracula and the Frank Langella Dracula were both based on the Hamilton Deane/John Balderston stage play. (There were significant revisions, but both movies are closer to the play than to the novel.)
vB apparently assumes that any punctuation at the end of a url belongs outside the /url tag and will put it there if you let it parse automatically.
Whoa! A mystery from my youth solved!
The Spanish version (in reality a dubbed version of the USA one! Unnecessary when a Spanish one was originally made, but the reason for that was the distracting accents in the original IIUC) I saw on TV in the late 70’s had the short ending when L&H ran away from the prison being chased by police dogs.
“What an odd way to end that short”, I thought, “I wonder if there were scenes missing”. Well, I wonder no more, the actual ending, as the German clips show, was for them getting a pardon for rescuing people from a fire, but that sequence was removed because L&H took refuge in a plantation among black people… with a now very racist “black face” disguise.
Semi-example: And Now for Something Completely Different, which consists of Monty Python’s Flying Circus sketches remade for the big screen. Cf. (e.g.) Nudge Nudge and Nudge Nudge.
“The Mark of Zorro” in 1940 and 1974. The 1940 version with Tyrone Power is one of my all-time favorites. The other one doesn’t make the list.
The same thing happens with nearly any punctuation at the end of a URL. The software here just assumes that the punctuation is part of the sentence rather than part of the URL, as that is most often the case. Wikipedia is rather unusual in using parentheses in URLs.
Beat me to it, I came in to mention these two versions.
A bit of trivia. When Gone With the Wind was finished filming Darryl Zanuck wanted to test it in front of a film audience, so the cans of film were transported to a theater. The manager agreed to show the film, and it was announced to the audience(who was there for Beau Geste, with Gary Cooper) that a new Hollywood movie would be shown in it’s place. The score for GWTW wasn’t completed yet, so the opening sequence of the film had the title music from 1937’s The Prisoner of Zenda.