Raph has posted about layers of game elements. I have replied, he has replied, I have re-replied, and I suppose he's likely to re-re-reply.
There are four layers, according to Raph, and it seems to be a fine distinction:
Mechanics, variations, theme, and narrative.
These all reflect on each other, providing and restricting how the others can manifest. In a simple example, the nature of the gameplay in most FPS games means that melee weapons are essentially useless, which restricts your choices of theme and narrative. It can just as easily go in the opposite direction.
The thing is, these are all one thing:
Gameplay loops circling the mechanics.
Mechanics are the basic rules of interaction and "logic". You can shoot, you can run, you can stack bricks, whatever.
Exactly what shooting, running, and stacking you'll need to dance with is a question answered by his "variations" layer. Here, you might have to shoot lots of little, fast guys at long range. There, you might have to shotgun a melee demon.
These variations provide the many methods of interacting with gameplay to keep things interesting. Sometimes, the rules are simple. In Tetris, the variation is "one of these six blocks will come next, at random."
I think this is intrinsically tied to "theme". Your theme guides your gameplay variation so closely they might as well be thought of in the same breath. You don't put much sword-themed into a ranged FPS, because the variation doesn't exist. You put gun-themed things in, instead.
But what drives these variations? When you get sick of "one of six random blocks", how does the game keep your attention?
Why, it puts variations into the variations. It leads the theme around by the nose, thus producing hundreds of new variations. As you go from level to level in a game, more than just the aesthetics change. Maybe one level is more open, allowing for more sniper work. Another has more puzzles. A third is about platforming. Any and all of these are gameplay variations which are "allowed" by the narrative. By which I mean, knowing the narrative makes the players think, "oh, okay, that makes sense" instead of "why am I surfing down the side of a pyramid?"
There is often more than one kind of gameplay mechanic, and the various gameplay loops interact with the various mechanics in various ways. This is what keeps our attention. These variations.
Here's the real question: is there a layer above "narrative"?