Various people have written of the limited number of types of translation from age old sense and word to John Dryden's metaphor, paraphrase and imitation to Roman Jacobson's tripartite of intralingual, intersemiotic and interlingual to Anton Popovic's four equivalences of linguistic word, paradigmatic, stylistic and textual. Translation is an intensely complicated issue that is deeply related to all aspects of the Kingdom Hearts franchise and all of the above divisions are both helpful and hurting toward understanding the stories.
Kingdom Hearts is itself somewhere between localized and translated between Japan and the United States. While the dialogue is in fact localized through a highly domesticating translation from Japanese to English (jokes are all domesticated/localized), the themes within the stories (innocence, transnationalism, Japan as Destiny island) are un'translated.'
The individual world stores are also translations (one might even call them iterations). By looking at the friction in the translations we can see important points. As usual, Atlantica provides one of the ripest examples, but I will also use Agrabah, Wonderland and Port Royal as opposing examples. Atlantica and Agrabah featured in Kingdom Hearts, Chain of Memories and Kingdom Hearts II; Wonderland features in Kingdom Hearts and Chain of Memories; Port Royal is new in Kingdom Hearts II.
Agrabah / Aladdin
Agrabah is one of the most used worlds. It features in KH, COM, KH2 and 258/2. Olympus Coliseum and Halloween Town are the only other worlds that share this distinction. All are interesting for their similar translated reasons. In KH, Agrabah traces the vague story line of the movie Aladdin with the minor addition that Sora is the hero and not Aladdin alone. You find Aladdin who has already found the lamp, Aladdin takes his two wishes, Jafar steals the lamp and becomes a genie with his third wish, you beat Jafar and finally you leave. There is the alteration that the cave of wonders is not where the middle of the level happens, but the end. COM repeats this with the minor intervention that you stay within Agrabah proper never going to the cave of wonders. Like the story and hinted at in the movie, but unlike KH, Jafar in COM is a rival for the Princess' affections (or at least desires the throne through her).
Aladdin is an addition to 1001 Nights that has been taken up by Orientalist fantasies around the world and adapted into many narrations. It in many ways has no original version. Thus, the two stories presented in KH and COM are equally presentable and readable. KH2 brings up something new as it is the translation/adaptiation of Aladdin 2, a direct to video Disney release. Iago turns good, Genie Jafar gets loose and Aladdin (Sora for the game) stops him. The second film has been loosely translated to parallel the game progression. Finally, 358/2 has various mini-stories that fill in certain gaps between KH and KH2 but has certain large differences. Whereas the physical layout of the city proper resembles the KH, it is completely changed in KH2. Similarly, the cave of wonders changes in all of the games.
Wonderland / Alice in Wonderland
Wonderland featured as an initial world in both KH and COM. In both cases the refrain from the Queen of Hearts angered at Alice for stealing her heart/memory serves as informative of the rest of the games. KH's theft of heart reveals information about heartless and the princesses; COM's theft of memory reveals about the nature of memory and the creation of false memories. However, it is absent from KH2. The translation from Lewis Carroll to Alice the film is awkward enough in its highlighting of certain sections and avoiding of others. However, even more particular sections are highlighted in the games. The Cheshire cat, the white rabbit and the queen and cards are all there, but all of the other notables are removed (including the caterpillar for obvious reasons despite his perfect inclusion into a game based on memory (COM) and identity (358/2).
As for the physical translation the entryway, the small/big medicine, the queen's court and the forest. All of the games have the same rooms. KH leads from entryway to small/big room to queen's court to forest to tea party; COM's main rooms are forest, but queen's court and small/big room are both boss battles; 358/2 adds a room between the small/big room and the queen's court that then leads off to two addition sections that are blocked off at first.
Port Royal / Pirates of the Caribbean
Port Royal is a translation of Pirates of the Caribbean the film, which was of course an adaptation of the Disneyland ride Pirates of the Carribean. The ride takes you through the idealized Caribbean tale of pirates attacking a town, taking gold, chasing women, auctioning off women, and going back to their booty cave; the film adds an idea of 802 coins of cursed Aztec gold that then curses the crew of the Black Pearl as well as entire sections about British Imperialism and the East India Trading Company, and then Davy Jones' Locker, the Flying Dutchman and Pirates as resisting modernity in the sequels.
The film is about the rescue of Elizabeth Swann by William Taylor with the help of Captain Jack Sparrow and the eventual raising of the curse of the Aztec Gold. These elements are all used within the KH2 world, but the imperialist and globalization elements are all avoided, as is the idea of pirates as good, freedom loving individuals. Instead, they are depicted as untrustworthy and generally negative. The elements that were transferred directly are the places and characters to provide a setting, and the curse and gold to privide an interesting battle mechanic (ghosts that are invincible outside of moonlight and a boss that is invincible unless all of the gold is in the chest).
Otherwise, the translation is some what odd in various ways: unlike the costume changes when visiting other worlds, Sora, Donald and Goofy maintain their normal clothes and cartoonish appearance despite the pseudo naturalistic representation of the Port Royal characters. Port Royal is, in many ways, a poor translation precisely because it is too close to the themes of capitalism, globalization and individualism, all of which are at stake within the Kingdom Hearts franchise. As those elements must remain hidden in the game there becomes little meat to use from an already limited story. That pirates are turned into the bad guys in the game despite such piracy and individuality being their specific allure to fans is equally confusing.
Atlantica / The Little Mermaid
Finally, we come to Atlantica, the adaptation of The Little Mermaid, which came from the Danish tale by Hans Christian Anderson. The original story involves a mermaid who gives up her voice to get legs, but loses the love of the prince, is unable to bring herself to kill him with a special dagger and in so doing dies (but gets to go to Heaven instead of turning into sea foam). The Disney movie names the mermaid Ariel, the sea witch Ursula and has certain machinations of Ursula directly opposing Ariel's quest for love as a means for her to gain the power of the Sea King, Triton. The story ends with Ariel and the prince falling in love and Ursula being banished (Disney's true love ending replaces the bittersweet soul to heaven ending). This story is translated almost perfectly (singing included!) in the KH2 world of Atlantica, but that version supposedly follows the two previous iterations in KH and COM, both of which follow different paths that culminate in the death of Ursula (poor thing dies the same death 3 times - 6 times if you include her large form and Riku's memory as well). The story is repeated but each time stresses a different element: first protectionism, second friendship and sacrifice, and third true love.