The Madagascar sequel goes the subtitle route by adding Escape 2 Africa. The third film has them going to Europe.
Rio 2, unlike the first film, takes place in the Amazon.
Films — Live-Action
B-movie action/martial arts movie series Best Of The Best. The first one involves crowning a champion of a martial arts tournament, hence the title. The sequel is a revenge blood-sport style movie, but the title can sort of still be justified. The third and fourth movies have nothing what so ever to do with martial arts competition: the third movie involves white supremacists trying to take over a small town, and the fourth one involved the Russian Mafia and counterfeit cash.
Only about half the Friday the 13th films are actually set on Friday the 13th.
The first Free Willy movie ends with Willy being set free, hence the title. There isn't a whole lot of freeing in the sequels. Unless the "free" there is supposed to be an adjective describing Willy. This was originally supposed to be averted, as the second film was going to be titled Willy 2: The Adventure Home (early trailers carry this title). It seems as if Warner Bros. got cold feet and became afraid that people wouldn't make the connection to Free Willy.
Home Alone. The first film fits this title perfectly. In the second film, Kevin isn't even at home, but he is alone. In the third film, Alex is at home, but isn't alone all that much as his mother is often at home as well. In the fourth film, Kevin is neither at home nor alone; he's at his future stepmother's house, which is always also occupied by the butler.
The Thin Man. The original film's title referred to the murder victim in the story. However, the sequels continued to use 'Thin Man' in the title, leading people to assume that 'The Thin Man' was the lead detective Nick Charles. By the time of the fifth film in the series, The Thin Man Goes Home, in which Nick and Nora go back to Nick's hometown, this was true.
When Neil Diamond did his remake of The Jazz Singer, he retained the original title, although he sings no jazz in the movie.
More an Artifact Naming Convention, the Carry On series began with Carry On Sergeant, a command familiar to all ex-servicemen or national servicemen at the time. It was commonly used by British officers, indicating that the sergeant addressed should proceed with orders given, or resume what they were doing before they were interrupted. Only a few of the subsequent titles came close to following that context.
Major League: Back to the Minors. Oh, there are major league ballplayers in the movie — the Minnesota Twins are the Opposing Sports Team, playing their own AAA affiliate in an exhibition match.
An interesting cross-language translation example happened with the Steven Seagal movie Under Siege. In Israel, the copywriters decided to translate the title as "Naval Siege", which sounded cooler in Hebrew. It also fit the movie well, because it takes place on a ship. However, when the sequel Under Siege 2 Dark Territory came out, they had a problem: the movie doesn't have a single ship in it. The result? The first movie is called "Naval Siege", while the second movie is called "Under Siege". Let the confusion commence!
The reason the book is titled The NeverEnding Story is left out of the film version. In the book, many vague allusions are made to the further adventures of secondary characters, always accompanied by the phrase, "But that is another story, and will be told another time." In the end, Bastian is told he can't leave until every storyline he started up is finished. However, several story hooks get created for every plot he wrapped up. Atreyu saves him by taking on the task on his behalf. In other words, the book has a very good reason why the story is neverending: because the act of writing a story creates a world where further adventures could happen, and telling those stories only creates openings for new ones. The human imagination has a limitless capacity for new stories. You couldn't actually film that, anyway.
Yes, you could: by narratively treating each element as an immediately apparent Chekhov's gun that is then abandoned.
Similarily, the title of The Inhabited Island is explained in the book (the protagonist, Maksim, thinks of the planet he crash landed on, as an "uninhabited island", and of himself as a "Robinson"), but not in the movie, making the title pointless.
Both movies known as Troll 3 have nothing to do with trolls. One is about radioactive plants (originally titled The Creepers), and the other is a Conan-inspired film also known as Quest for the Mighty Sword.
The Karate Kid (2010) remake does not feature any karate, and when the primary character's mother talks about him learning Karate he explicitly states that it is Kung Fu, not Karate. Press releases have explained that the other characters gave him the derogatory nickname 'karate kid' because he claimed to know a little bit of karate early in the film, but he was never addressed as such in the movie itself. The film was released as The Kung-Fu Kid in several countries. In Japan & South Korea, it was called The Best Kid.
The remake of The Manchurian Candidate doesn't have anything to do with Manchuria. The writers justify the name by involving a corporation called "Manchurian Global" in the plot.
Die Hard in Poland and Italy has this. The title there is Glass Trap (Szklana Pułapka and Trappola di cristallo, respectively), which makes sense, since the first one takes place in a skyscraper. Not so much in the sequels. The same happens in Spain. The title there is Crystal Jungle (Jungla de Cristal). Latin-America was relieved of the problem, as the movie there was called Duro de matar (Hard to kill). Russian version brilliantly replaced an idiome with an idiome, being called Крепкий орешек (A hard nut to crack), but the sequels had to go by numbers because of that.
In Poland, The Hangover was re-titled Kac Vegas (The Vegas Hangover and a wordplay on Las Vegas). When the second part did not happen in Vegas anymore, the distributors decided to title it Kac Vegas w Bangkoku (The Vegas Hangover In Bangkok). Everybody laughed.
Zig-zagged by the Police Academy movies. The first took place at the title's academy. The second only had a brief scene there. The third and fourth took place there. The fifth and all subsequent films had brief scenes at the academy at best. The series tried to make the title relevant with subtitles like "Their First Assignment" and "Back in Training," but ultimately gave up as later installments took the action to Miami Beach and Moscow.
The Mummy: Tomb of the Dragon Emperor did not feature the title character Imhotep ("the" Mummy). The villain was a mummy, but the movie might have been better titled "The Adventures of Rick O'Connell".
Rush Hour. There's only one scene in the first movie where the title makes sense. As for the sequels, what does "rush hour" have to do with the crimes around the world?
Back to the Future has some in-universe examples of this. In 1955, Lou's Café is a café owned by Lou Caruthers. By 1985, it has become Lou's Aerobic Fitness Center and, given his age in 1955, Lou is probably no longer the actual owner of the building (or if he is, he's just collecting rent money). Twin Pines Mall (or Lone Pine Mall, depending on which timeline you're in) was named after the tree farm which used to exist on the land. Twin Pines Ranch being changed to Lone Pine Ranch after Marty ran over one of the display trees is an example of averting this trope, resulting in the irony that the name later becomes the artifact anyway when the mall is built.
The Bourne Series started off fairly clear with The Bourne Identity being about Jason Bourne trying to understand what he is, the two sequels The Bourne Supremacy and The Bourne Ultimatum don't really make sense given the stories, but are a part of the book titles and thus they were kept. Some feel that had the titles been reversed for the second and third movies, they might have made more sense. The second film was Bourne telling the government to leave him alone (giving his "ultimatum"), and the third film was Bourne destroying the government conspiracy surrounding Treadstone (showing his "supremacy" over the government officials involved with it). The Bourne Legacy stretches this even further, starring a new character not named Bourne (the "legacy" is the aftereffects of Bourne blowing up Treadstone).
North By Northwest is a partial artifact title. On one level, it makes sense since it refers to Hamlet feigning madness as Cary Grant does. But on another level, the original draft of the script had set the ending in Alaska. The title only sort of made sense as a compass direction for the film's action in the original draft, but even less so when it was changed to Mount Rushmore.
The film adaptation of Stephen King's short story collection Hearts in Atlantis is a fairly close adaption of the story "Low Men in Yellow Coats" (which takes up the bulk of the book), but it has nothing to do with the eponymous short story "Hearts in Atlantis". "Low Men in Yellow Coats" is about a boy who befriends a Cool Old Guy with psychic powers and tries to protect him from the mysterious men pursuing him, and "Hearts in Atlantis" is about a bunch of college kids who waste all their time playing Hearts (the card game) in their dorm room (which they call "Atlantis"), thus making the movie's title a bit baffling.
The Haunting in Connecticut 2: Ghosts of Georgia, as in the state, not a character. The entire film takes place there. Apparently the original title was The Haunting in Georgia before the suits decided the brand was more important.
The Three Stooges were originally the supporting act for a comedian named Ted Healey and were called "Ted Healey and His Stooges". This made sense because a "stooge" is an insulting term for somebody who serves under somebody else and can also mean being the butt of a comedian's gags. But early on in their film career, the Stooges broke up from Healey and became known as The Three Stooges, even though they were no longer stooges to anybody. Averted in the Spanish versions, where they are known as "Los 3 Chiflados" (The Three Crazy Men), and are never referred to as stooges to anyone.