Dark World
The Dark World, also referred to by such terms as "Evil Realm", "Dark Realm", "World of Evil", and "Underworld", is a dark, twisted realm that serves as Ganon’s territory. While the English version gives it various different titles, the Japanese version has two names for it.
The first and more specific title is “Makai”, literally meaning Demon World. Not to be confused with hell, a Demon World is any territory ruled by a “Maou”, or Demon King. Ganon is the only known Maou in the Zelda series, as his various titles include the word Maou in every game, and no other character has such a title. Thus, in Zelda, a Makai is any territory ruled by Ganon.
The second title is the less specific “Yami no Sekai”, meaning World of Darkness. Much closer to the English translation of Dark World, it is also closer in meaning. A Yami no Sekai is any realm full of darkness. These terms are, however, occasionally used interchangeably in the Zelda series.
The Sacred Realm, apart from a few sections of Hyrule itself, is the only place confirmed to have become Ganon's Dark World in any game, but several games leave its location up to the imagination of the player.
Legend of Zelda and Adventure of Link
The original Legend of Zelda makes no direct reference to Ganon's Dark World, but Ganon's title of Maou implies the existence of one. The game speaks about the Underworld, but the Japanese word used here is "chika", which is a literal underground lair, and not specifically a Makai.
Adventure of Link also talks about the Underworld, but this time, the Japanese word used is Makai. Whether the underground lair of Legend of Zelda is the Dark World of Adventure of Link or not is unknown.
A Link to the Past
In A Link to the Past on the Super Nintendo, the Dark World is a corrupted or reversed version of the Golden Land that is created after Ganon reaches it and wishes on the Triforce. It is known that the Golden Land is a mirror that reflects a person's true self, so Ganon and his minions are turned into monsters when they enter the Golden Land, and Link turns into a rabbit unless he has the Moon Pearl. When Ganon takes the Triforce, he wishes to rule the world, and the Triforce grants that wish by turning the Golden Land into his Dark World. When that happens, Hyrule is referred to as the Light World.
The Dark World of A Link to the Past is referred to as a Yami no Sekai, and thus, is not necessarily a Makai. However, Ganon is a Maou in the game, and he clearly has rule over the Dark World, so it matches the description of a Makai.
In the game's ending, Link defeats Ganon and approaches the Triforce. The Triforce tells Link that Ganon's defeat will cause the Dark World to vanish.
Ocarina of Time
In Ocarina of Time, Ganondorf tricks Link into opening up the entrance to the Sacred Realm by opening the Door of Time and pulling the Master Sword from its pedestal. This causes Link to be sealed inside the Chamber of Sages until he is old enough to wield the Master Sword, and allows Ganondorf to enter the Sacred Realm.
As Zelda later tells Link, when Ganondorf entered the Sacred Realm and touched the Triforce, he became an "Evil King", and the Sacred Realm became a "World of Evil". Here, the Japanese version actually calls Ganondorf a Maou, and the World of Evil a Makai. Rauru gives a similar account of the event. However, after Ganondorf transforms into Ganon, and is defeated by Link, Zelda calls for the other Sages to seal him in the corrupted Sacred Realm, and refers to it as the Yami no Sekai. Thus, though the two phrases have different meanings, they are interchangeable to an extent.
Oracle of Seasons and Oracle of Ages
The Dark World is given only a minor mention in the Gameboy Color game Oracle of Seasons, when main antagonist Onox reveals that he was summoned from the Dark Realm by none other than Twinrova[1].As with A Link to the Past, the term used here is Yami no Sekai.
Oracle of Ages' English translation states that Veran has extended the reach of the Dark Realm, however, that was a misstranslation. The term used there is not "Yami no Sekai", but conversely, "Sekai no Yami". Thus, Veran only extended the "darkness of the world", and not the actual Dark World.
Four Swords Adventures
The Dark World exists in two different forms in Four Swords Adventures. The first is a tainted, parallel world to Hyrule, and the second is it's extension into Hyrule.
Though its parallel existence to Hyrule is similar to the Dark World of A Link to the Past, the two differ in several ways. The Dark World of Four Swords Adventures is accessed by Moon Gates, most of which need to be activated by Moon Pearls, whereas in A Link to the Past, the Dark World is accessed by blue portals, and can only be exited by the use of the Magic Mirror, an item absent from Four Swords Adventures. Moon Pearls are used in both, but for different purposes.
The second form of the Dark World is the fifth level in Four Swords Adventures. It consists of three stages: The Lost Woods, Kakariko Village, and Temple of Darkness. It is named so, because it has become completely overcome by darkness.
At the end of each stage is a barrier that can be broken if the four Links have obtained a certain amount of Force Gems. These barriers drain the Force from Hyrule, and if not destroyed, they would eventually transform all of Hyrule into the Dark World, because they are connected to it[2].
Both forms of the Dark World in Four Swords Adventures are referred to as Makai and Yami no Sekai interchangeablly.