For me, roleplaying is about making choices. I hear there exist alien entitites called other people who disagree. Whatever.
Large heaps of rpg theory are also about choices. More probably, I remember those ones better, but again, whatever. I’ll go through a few from this point of view.
GNS is about the kinds of choices people (in groups) want to make. I am not an authority on the subject, but am fairly likely to get G and N approximately correct. I think these are useful not because they are a tool for putting people in boxes (which they technically speaking are not, but which is a very easy extension of the theory, but instead because you find out that there actually are people who enjoy these kinds of choices, and including them in games to see if people enjoy them might be useful. That’s my opinion.
In a group with a gamist agenda, people appreciate most the kinds of choices that show off your sense of tactics or guts or something like that. These are usually related to winning or beating an obstacle.
A group playing in narrativist way people most appreciate choices that reveal interesting parts about the characters’ inner life. Such decision points often manifest as moral dilemmas and sometimes may involve playing suboptimally from fiction or rules POV (note the qualifiers; they matter).
A group where simulationist play happens most appreciates, well, uh.., I’m not actually quite certain. I’m trying to do a positive definition here. Maybe choices which reveal interesting about the way the fictional reality functions? I guess that is good enough.
GDS aka Threefold
John H. Kim has done a great summary of the threefold model, as has Silvered Glass of rpg.net. From my perspective, threefold talks about the heuristics game masters use when making choices. I will blatantly extend this to players, too. Note that the categories are not mutually exclusive; rather, an overt focus on one will limit the others, because usually there are situations where following a different heuristic would lead to different consequences. I think it is useful to analyse one’s gaming based on these categories. I also think it is useful to check out systems based on thse categories, especially to see if some of the GDS styles will conflict or are congruent in a particular game.
GM with gamist tendencies is someone who tries to make choices so that the game is challenging to the players. My extension is that a player with gamist tendencies wants to make choices which overcome the challenges. Note: Rules and fiction can both be used as the method of presenting the challenges. A courtly intrigue can be as good a gamist challenge as a series of bloody skirmishes even in a game with few to no social rules.
Dramatist GM or player makes decisions that result in the best story (or tries to, anyway). This can be a railroad or a more collaborative exercise (I certainly prefer the latter).
Simulation as a preference means that the participant will make decisions based on “what would really happen”, given the diegetic (in-game) reality.
The AGE model by Kuma takes a look at roleplaying from ecological POV, in that the environments that play takes place in are emphasised. This post will not make much sense unless one is somewhat familiar with the model. The six forces are essentially created by players with given decision-making heuristics. Choices are constrained by the different spaces (em, a, game, play) and also affect those spaces by setting precedents and opening new potential interactions.
Rules can align some priorities. If, for example, the rules are designed to help in creating a story through challenges, they can be enjoyed by people whose styles of play might normally conflict. Setting likewise; if all characters have a drive to prove themselves by doing the impossible and also want to become as powerful as possible, realistic behaviour in that setting corresponds to facing and triumphing over challenges.
Both of the above effects are achieved by constraining some choices and creating new ones. Rules and setting do both.
In traditional play (huge sweeping generalisation incoming) GM is the one who thinks about the good of the game as a primary filter that removes choices, or such is ideally the case, at least. Personally I don’t see the point of not assuming that players also want the good of the game. I do, as a player, to some degree. Many people who both run and play in games probably think more holistically and act in the best interest of the game.