Lorule, the "Dark World" version of Hyrule in A Link Between Worlds, bears an extreme resemblance to the Dark World from A Link to the Past.
(ALTTP spoilers follow:)
However, in A Link to the Past, the "Dark World" was actually the Sacred Realm, twisted into an evil form by Ganon using the Triforce's power, and is later reverted to the unspoiled Sacred Realm (or "Golden Land") after Link recovers the Triforce, undoing much of Ganon's evil influence over the land. This is canon in A Link Between Worlds' world, as shown by the murals depicting the events of ALTTP in Hyrule Castle.
Lorule seems to have a different backstory as an "alternate version" of Hyrule, and even has its own princess.
(ALBW spoilers follow:)
We know that Lorule has its own history, its own royal family, its own Triforce equivalent and its own Sacred Realm. Hyrule's Sacred Realm has none of these things, so it seems clear that Lorule is something completely different than ALTTP's Dark World.
However, much of the geography of Lorule is near-identical to the geography of ALTTP's Dark World, including landmarks that aren't present in Hyrule at all, such as the Thieves' Village, the Skull Woods, Misery Mire, and so on. In addition, most of the monsters are identical to the ones found in ALTTP's Dark World. This is all despite the fact that from a story perspective, these two Dark Worlds are actually two different places, and seem to have no direct relationship.
Obviously, from a game design perspective, the two realms are designed similarly because A Link Between Worlds is deliberately aping A Link to the Past from top to bottom, including to its geography, dungeon concepts, monster design, items, and music.
However, from a story perspective, is there any official canon explanation for these similarities? Is there any direct connection between ALTTP's Dark World and Lorule, or is it just a "coincidence" that they share so much in common?