more theory models - what makes decisions and what drives the game?

So, Zac is continuing to slowly and meticulously vivisect the GNS essays, and this has got me thinking about the different ways we can divide games up. I don't really have an overarching theory of gaming, but I do have the basic categories I tend to put stuff into. These are largely based on my own observations and prejudices.
Worth noting that when I say games, I mostly mean a specific group playing a specific system. The way I run (say) LotFP is probably very different to the way the next person does it.

First up, what controls the game? When an outcome is doubtful, how do you decide what actually happens?
You can divide this into three rough categories: crunch, shared narrative, and fiat (and then also hard skills sort of). 

In a crunch-based game, there is almost certainly a specific mechanic for what you want to do. Players interact with the world and the ongoing story through game rules and often by applying specific character powers. Mechanics are carefully balanced so that the 'right' outcomes are probable or guaranteed (...if the designer did their job properly). You often have a broad underlying mechanic, and then loads of modifications to it for different situations. These games tend to put a lot of focus on character builds. What you can and can't do is strongly defined by the decisions you make in character creation. Often, a skilled optimiser can make a character that's much stronger than an unoptimised character. These sorts of games tend to involve a hefty character gen (maybe taking up a whole session or more) spent pouring through books comparing options, and then in play fairly strict adherence to the rules. In play, there tends to be a lot of focus on working the system in your favor, so that the raw mathematics of the situation rigorously defines what happens.
Rules-mastery and character optimization are how you get ahead. Combat is often a focus, there are typically huge amounts of books for this detailing ever more options. It's the kind of game that encourages spreadsheets.
Ultimately, here, when something is in doubt, you apply game mechanics to find out what happens.
Vampire the Masquerade is an example of this sort of game that I like, Pathfinder is an example that I don't.

Shared narrative-based games (AKA storygames, narrativism, wank etc) are focused on deciding who gets to decide how things play out. The system is there to determine who gets narrative control, and the GM's power to decide world details and outcomes is spread among the players more evenly. Games without GMs, or which give players a lot of tools to take over GMing fit in here nicely. It's all about collaborative storytelling.
Usually, the mechanics are pretty abstract and universal. You tend to get the ability to force the story in particular directions and control over things that aren't your own PC. These games have much more of a tendency to think of themselves as Art, and to deal with genres that aren't variations on action, horror, fantasy and sci-fi. 
These games require a lot of creative input and a lot of buy in. All of the worst experiences I've had in gaming have been with these games, because by exposing your ideas for others to judge in the sorts of creative struggles these games produce, you inevitably let yourself be emotionally vulnerable to the results. So have a few of the best; when everybody is firing on all cylinders you can get some cool results.
An example I like is Monsterhearts, an example that made me want to pound nails into my eyes was Ten Candles.

Last up, we have fiat-based games. This is where the OSR style is focused. Outcomes are mostly decided via the GM making a judgement call and often an ad-hoc rule. Rules are minimalist, and tend to focus on things that are hard to make fair judgement about (magic because there's no real-world version to refer to, character death because of the stakes, violence because it's so complex and there are also high stakes).
Character gen is usually fast, because the mechanics are comparatively unimportant. In-world details are more important than game mechanics: if you can find or make a ladder, you'll climb easier. This goes back to the 'GM's rulings' thing: any mechanical effects are adjudicated by the GM based on specific circumstances.
Player skill tends to be an important concept here. A player who comes up with smart ideas is likely to succeed, regardless of their actual character strength. Game balance tends to be a low priority, as that artificially restricts the GM's ability to make an accurate ruling, and means that player skill would need to be minimized if they do something 'too good' or 'too stupid'.
If you're reading this blog, you probably play this sort of game. 

(in larp, there is a fourth category: hard skills. Which is to say, there are few game mechanics or storytelling tools: to do a thing, you actually fucking do it. In one of my favorite games, Odyssey, pretty much everything was hard-skills based. Fighting was done by smacking your enemy with a prop sword, religion was done by actually performing ceremonies and hoping that the members of the plot team watching were impressed, thieving required you to sneak around the camp at night while people were sleeping, and so on... you see this sometimes in tabletops, such as in things like riddles, chess puzzles and talky social bits, but it's less common and normally the game has another system so the fights don't descend into unplayable freeform anarchy)

Although different games focus on different styles of decision making, there's overlap. I find Vampire tends to be hardskills social scenes and politics, and crunchy combat and powers. Likewise, fiat-based decision making is inevitable at least a little, because no game can cover every circumstance.
Ultimately, this distinction is about where the power lies in the game: with the game's rulebook, with an agreement to share creativity, with the GM's judgement, or just 'well actually do it then'.

The other distinction I tend to care about is what the game is about. What are we here to do, where is the fun in the game? Where are your goals and what will drive things forward? Again, I'd divide this up into a few categories: challenges, finding stuff out, characterization and plot.

Challenges is pretty self explanatory. There is an obstacle or danger, and you need to overcome it. This is most purely expressed by your crunchy tactical combat of 4th edition D&D. Here is an encounter: beat it. You get your fun by taking on an obstacle and winning. This is the 'challenge based' play a lot of blogs talk about, or what GNS is pointing at when it talks about gamism.

Finding stuff out is also pretty easy to grok. It's your mystery games like call of cthulhu and gumshoe. It's also exploration-based games. This is how I tend to run something like Wolf-packs & Winter Snow, and what The Garden's Of Ynn was all about. You keep playing because you want to learn what's over that next hill, what the next dungeon level down is, how deep the conspiracy runs... 
Finding stuff out is also, tbh, my where my fun tends to be. I like learning about things, I like putting information together. 

Characterization is focussed on the PCs, their personalities and their interactions. You roleplay the shit out of your character, and see how that ends up. Games driven by this stuff care about the PCs backstories and personal philosophies and what links them together. Often, low-level social PvP happens, but violent and lethal PvP is unlikely. Every time I've played Monsterhearts, it's been like this. I often find Vamp tends to go this way, to; I think it's something about playing a monster that makes you really want to get IC and explore that character.

Plot is, you know, plot. There is a story ark, and we are going to play through it. At it's worst, it's going to end up as a horrible railroad. Of course, if you're sensible the plot develops as you go. This is, I think, how WW expected Vamp to be played, but not how it usually ends up in my experience.
I'll be honest, if I want a plot, I'll just read a novel. RPGs scratch other itches much better. Your mileage may vary, though.


So yeah. That's how I tend to divide stuff up and describe things. Like 'oh, VtM is characterization driven and crunch based' or 'wolfpacks is exploration driven and fiat-based'. 
These are only rough thoughts. I could put them into a better essay, but I'm lazy.