Many thanks to Gary Susman at Entertainment Weekly‘s Popwatch blog for correctly stating that Hotel Chevalier, the Wes Anderson short film that was recently made available to American iTunes customers, is a “prologue” to The Darjeeling Limited.
I have seen many, many people refer to it as a “prequel”, but it is not. A “prequel” is a sequel that takes place before the story being sequelized. And a “sequel” is a story that is told after another story.
So, for example, Indiana Jones and the Temple of Doom (1984) is a “prequel” to Raiders of the Lost Ark (1981), because it is told later but takes place earlier. But neither of those films could possibly be a “prequel” to Indiana Jones and the Last Crusade (1989), which takes place later and was told later.
Likewise, J.R.R. Tolkien’s The Hobbit is not a “prequel” to Tolkien’s The Lord of the Rings, because The Hobbit was written first. However, just to complicate things, if Peter Jackson were to make a film version of The Hobbit, then it would — or at least could — be a prequel to his film version of The Lord of the Rings (2001-2003), because the films told the stories in reverse.
At any rate, Hotel Chevalier was filmed a year or two before The Darjeeling Limited, and it takes place earlier, too, and it has been released earlier, as well. So, it is not a “prequel”. It cannot be.