When trying to categorize and describe gameplay experiences, there's one huge difference in experience that I've been thinking about lately, which is the difference between an isolated and repeatable gameplay experience and between the long-term experience of progressing a game.
The former experience I think I'll refer to as a gameplay instance. Note that I'm making up these terms as I go along, so if someone has better ones for me to use, let me know. A gameplay instance includes the decisions involved in completing a specific task, usually in a single gameplay session - like "take the opponent's king" or "roll up the largest ball possible." As I'm describing it, gameplay instances are layered on top of each other - completing the task usually involves completing minor objectives along the way ("lure the opponent out of his defensive position" or "get onto that hill so I can pick up the stuff on top of it").
So with a definition of an "instance" that broad, what is left? The unspecific goal - "progress the game." Usually progressing the game involves completing specific tasks, but there's a separate experience that emerges out of these specific tasks that is more than their sum. In a Final Fantasy game, each battle is a gameplay instance, and navigating a dungeon is a gameplay instance, but then there's the motivation to see what happens next driving you even when you're tired of killing your 300th zombie dragon. That's the gameplay sequence at work.
So while most games these days include both kinds of gameplay experiences, they emphasize each to different degrees. Games far on the instance side include almost all board games, and games like Left 4 Dead that emphasize repeatable mutiplayer experiences. On the sequence-heavy side of things we have adventure games and interactive fiction. Between the extremes we have most modern games, which include overcoming challenges as part of an ongoing progress toward an uncertain final goal.
So I intended to say more, but I think I'll just stick to this for now and come back to it. Generally speaking, the point is that figuring out early on what kind of experience you want to provide and focusing on elements to provide that is important, and among other things you should figure out to what extent you want to emphasize a instanced or sequential experience.