Here's a vague attempt at the categorization of various GM-Player conversations (conversations, that's the word I've been looking for all this time). I'm making it up as I go along, so it might be completely wrong or misleading. But I'm trying.
The Mountain Expedition - Here the PCs either have a place in the world (heroes, priests, investigators...), an overarching motivation (gold, revenge, truth...) or an mission-dealing boss (MI6, Adventurer's Guild, god...) or some combination of all three as part of the pre-negotiated premise. This orients them to the "top of the mountain". There can be many different ways to get to the top and the PCs can stop anywhere along the way, or go back to the valley for stuff but their objective should always be clear (implicit or explicit ingame). The GM's job is to present the mountain as well as he can, particularly making it clear when the way is going upwards and when downwards. He should make the mountain hard to climb, but not as hard to be impossible, nor as easy for it to be boring.
The Pinball Machine - Similar to above but instead of a single mountain, there are at any one point a number of blinking, lights, slopes, tunnels, windmills and who knows what else that the PC-ball can go hit. In any case too many to deal with all at once. Lights go out if the PCs miss their opportunity or deal with other stuff and new challenges present themselves as a result of previous actions or sometimes randomly. The PCs don't necessarily start with any clear ambition but are propelled into the world by means of a spring, giving them motion, and any subsequent motivation is a complicated result of bouncing and colliding with stuff. There is no top of the mountain, but there's the same motivation of piling up points instead of altitude.
The Exhibition - There is a large building that the PCs wish to visit and explore. The building has many wonders inside, which are visited by following the trail, stringing the exhibits into a thematic whole. Sometimes rooms might be rushed through, and in extreme cases seen out of order reverse or there might be whole floors missed, but there is a whole picture. The PCs are able to fiddle with some exhibitions, but are mostly not allowed to touch. They can act and react to what the building presents, going along with it, following the prompts and clues.
The Train Murder - The PCs are presented with challenges and mysteries on a moving train. These occur on the train and the murderer has not left it, so everything occurs on the train. It is thus only a matter of time before the murderer is found, after the appropriate number of conversations have been held and clues gathered. There can be views and towns along the way, but they have little to do with the PC's actions, as do the events. Another murder may occur for example, when the train reaches a certain destination.
The Burning Rooms - The PCs are in a burning house, quite probably one they've set on fire themselves, and they must make choices. What to save and what to leave. Perhaps even to perish in the flames, heroically (or foolishly?). Whatever they do will tell something about themselves, about the world they live it. Except when they exit the room, they are in another burning room with new, but similar choices. What kind of person will come out of the house? Heck, the world's on fire.
The Russian Roulette - The PCs are trying to get something or somewhere, either way, they've got some motion and then someone places a gun in front of them. It might not even be loaded, or maybe they've got to shoot at someone they love instead of their head, or maybe at their foot. Point is, shoot the gun or turn back. And they need to ask themselves if it's worth the risk, they need to ask how much they want it. And whatever they do they move in some new direction where there will be new guns and new corners to turn and consider.
So, as I said, I might be wrong about these. But if someone asked me how to run a game, or how to make a game work, or where a game was going wrong, I'd ask them which one of these they were playing. And after that, adjustments to either Player of GM actions/expectations to match.
You might notice that these types come in subtle pairs. The Mountain and the Pinball are really two sides of the same coin as are The Burning Rooms and the Russian Roulette or the Exhibition and the Murder Train. Some might also mix and match better. The Exibition and the Burning Rooms might have some superficial similarities but they are super-incompatible. If a player comes into an Exhibition expecting a Burning Room, he'll be setting off alarms left and right and getting tazed by guards in no time. Likewise a GM trying to pull a Russian Roulette on a Mountaineer player will likely feel let down by the logistical solution, even while the Players are expected to do almost the same thing in both. On the other hand the Burning Rooms and The Pinball are rather similar and can definitely mesh to a degree. The Mountain and the Murder Train are also incredibly similar, to the point where a few minute changes can make them indistinguishable. The Exhibition can become a Mountain if the "big picture" of the building is something that can be discovered with work, cunning and skill instead of being laid out merely in time.
Does this make any sense to anyone?