In my experience -- a dangerous way to begin, but safer than feigning someone else's experience -- a group of players want to do one thing: everything.
It could be that each group has a fixed number of ideas, regardless of size, so no matter how many mouths are moving 12 ideas come out in response to every situation. A GM has to wrangle these ideas and these players. Like butterflies, they light on every surface and then flitter away. Poetry, but with battleaxes and cybernetic arms. To encounter an in-game situation with any reasonably conscious group of players is to drink from the firehose of inspiration.
Someone called Daztur has written a long, cogent, useful analysis of two different ways that roleplayers handle combat. Using concepts drawn from MMO players, Daztur posits "combat as sport" vs. "combat as war." Go read it if you need those defined. Useful concepts, these. They explain a lot about different perspectives on The Right Way To Play and also What Fun Really Is. And they fall short of the mark.
Players have ideas. Lots and lots and lots of them. Players think different things are fun, lots and lots of things. Often a group of players will be gnawing on both the Sports approach and the War approach to deal with a challenge. Often a single player will argue in favor of both during the same sentence. All it takes is the flap of a butterfly's wings to tip the decision in one direction or the other -- or both, or something else, as players are an infinitely creative lot.
That's the problem with Daztur's analysis, cogency aside, and with a lot of the discussion surrounding it. A group of people who automatically default to one approach or t'other sounds like a group that's, well, kinda boring. If you're always turning your environment into a weapon, you're neglecting your character. If you're only using your character's abilities, you're missing out on the world. Or so I'd guess. In my experience, players don't settle on one approach for long, and GMs shouldn't assume otherwise.