So the standard question is "What's your favorite Christmas movie?" My standard answer was Die Hard until it became In Bruges which I like much more.
These responses are funny because they're not really Christmas movies in the sense most people mean. And yet both qualify by actually taking place at Christmas.
This confusion is amusing, but I can fix it. As my gift to you this season, I present the Christmas Hierarchical Ring Index System Tracking Movies And Stories (CHRISTMAS; since this is still indevelopment, I call the current version eXperimental Movie Arrangement System, or XMAS).
XMAS is a system for describing, in terms of hierarchical "Ring" domains, how integral Christmas is to a movie. Rather than explain further, I'll describe the rings. I will also not discriminate against TV specials in this hierarchy, and there appears to be no reason it couldn't apply to any narrative, including novels and even songs.
Ring 0: Christmas Movies
A Ring 0 movie features one or more widely-accepted major characters from the tradition of Christmas as a major character in the film. In other words, if the movie has the newborn Jesus, 3 wise men, Santa Claus/Pere Noel/Sinterklaas, flying reindeer, or Krampus in it, and they or their part of the Christmas tradition are key to the plot, then it's Ring 0. These are movies that are not only related to Christmas, but they inherently are tales about the Story of Christmas.
A grey area would be recently-manufactured Christmas legends. The classic example is Dickens' "A Christmas Carol," where we meet the ghosts of Christmas Past, Present and Future (and importantly, no traditional Christmas figures like St. Nicholas). The characters, however inherently Christmas-y, are Dickens' own invention. For that matter, reindeer appear to have become a normal part of the Christmas story only in the 19th century, but further research is needed.
Note also that technically, such a film might not even have to take place during Christmas Day to be a Ring 0 film, such as a song or story that only dealt with the Magi, who traditionally arrive after the birth of Christ.
Examples: The Nightmare Before Christmas, Rudolph the Red-Nosed Reindeer (Rudolph is a very recent invention, but the reindeer are not, and Santa himself is a key character in any case), Fred Claus. Life of Brian is an interesting case, since it starts on Christmas Day (Brian is born on the same day as Jesus, in the stable next door), and even features the Magi. However, these times and characters are largely peripheral to the main story of the movie, which follows the parallel lives of Brian and Jesus. Similar arguments would apply to any life-of-Jesus story where the Nativity was only the introduction to the story.
I will also note that movies about department-store Santas do not fall into Ring 0, but we must note the case of Miracle on 34th Street, where the Ring classification of the movie depends on whether you think the film's "Kris Kringle" is the real thing or a deluded old man (the movie isn't particularly ambiguous, but there's room for an argument that Kringle was deluded but rich; if so, it moves from Ring 0 to Ring 1).
Ring 1: Movies about Christmas
A Ring 1 story does not tell some variant of the traditional Christmas stories, but the story is so inherently intertwined with the celebration of Christmas that it the plot is unimaginable without Christmas. Obvious examples are Jingle All the Way, A Christmas Story, and A Charlie Brown Christmas.
Ring 2: Movies at Christmas
A Ring 2 movie takes place at Christmas, and Christmas is at least peripherally part of the imagery or plot of the movie, but Christmas is not inherent to the plot. My beloved In Bruges and Die Hard fall into this class. 2046 too. "Takes place at" is subject to some discussion, but I'd say the purest definition is that the movie must have at least one scene that is explicitly in the 12 days of Christmas. Christmas Eve movies arguably deserve inclusion here, but I'd want to see an example first.
Ring 3: Movies that relate to Christmas
If the movie does not take place at Christmas, but mentions Christmas or Christmas activities (presents, Santa Claus) in a way that is inherent to the plot, then it falls here. I can't think of any examples at the moment. Any movie centred around Advent would probably fall into this ring. A theoretical movie about training to be a department-store Santa Claus that didn't actually have any scenes in the Christmas season would qualify for this ring.
Ring 4: movies that mention Christmas
Any film that mentions Christmas or Christmas activities or any element of a traditional Christmas story, but doesn't otherwise qualify for Ring 3, falls into Ring 4. As a notional example, if Point Break had featured Santa masks instead of ex-presidents, it would be a Ring 4 movie.
Ring 5: movies that take place in a narrative world where Christmas exists
This would include any movie set in our world (or one very much like it) after 0 AD.
Ring 6: movies that take place in a world where Christmas has not yet happened, or does not exist
In other words, any movie set in the pre-Christian era, or any fantasy or science-fiction film clearly set in a world that does not have Christmas. Examples: the Star Wars and Lord of the Rings series. (One might point out that Star Wars takes place in our universe, merely long ago and far away, but as far as I can tell, it explicitly takes place in a realm where none of the characters would have any knowledge of anything in human history, and that's enough for me to consign it to Ring 6). If you want to ask about time-travel or alternate universes, the guideline is that if any character has spent any time in the light cone of Christmas, it's not Ring 6. If the alternate universe contains an event that is recognizably Christmas (or is so similar to our world that the existence of a Christmas seems implicit) then it's not Ring 6.
Finally, be aware this hierarchy says nothing about the quality of the story.