I've been at work on Workplace, my proposed entry for this year's Game Chef contest and I got to thinking about how essentially abstract it is: you play a bunch of characters connected by the place they work and most of the interactions between them are about their shared workplace and their relative status within it. The characters aren't defined by the system though: there are no stats, no skills, no advantages, no equipment; you don't need to know where the other characters are standing or what's nearby, because if any of those things become relevant to a scene, you just narrate them in as convenient, as long as you're honest & plausible.
On the other hand, all those things are relevant in The 'Hood: the fiction depends on knowing what you can do, it relies on a largely intangible model of the game-world that defines what is and isn't possible for your character to achieve. If you want to pick a lock, you have to have a move that justifies you doing that (cover your tracks comes to mind) but you also have to roll with your stat to see what happens; before any of that though, you have to be standing in front of that door...with lock-picks.
It's a significant difference in approaches: in the latter game, there's a lot of negotiating and positioning between the players and between the player and the MC before they can get into a situation where it's even plausible that they could attempt to pick the lock. In the former game, you just say something like "I'm going to pick the lock on the storeroom, I just want to know whether I'm caught doing it or not." Bish-bosh, job done, no messing around, cut right to the chase (literally, if it turns out you do get caught.)
Neither of these approaches is any better than the other, they are just different ways of handling the model of the game and the story it tells: games powered by the Apocalypse World engine, like many traditional RPGs, derive the story from the model. You set things up, then you explore how they interact at a mechanical level, like setting the parameters for a simulation then leaving it to run by itself. Afterwards, you can look back at what happened and extract the story of those interactions within the model: "Agent A acted on Object B with Cause C which had Effect D; as a result, Agent E was able to use Effect D to facilitate its interaction with Agent F..." and so on, only with more blood and tears if the story is any good.
In a traditional RPG, this telling of the story after the interactions of the model have taken place occurs immediately after each interaction: you're not just rolling dice in a vacuum and stringing the results together at the end, each result feeds back into the story right away. As we follow the emerging narrative, it effects change within the model, allowing for more interactions and so on in an unpredictable process that should inevitably build towards significant, permanent changes within the model (and therefore the story, etc.)
Coming back to Workplace, what it shares with a lot of contemporary story telling games is that the story comes first and the model is largely derived from that, not the other way around. If I'm playing a character in one of those games and I want to pick the lock, I still need to have lock-picks, but I don't derive the existence of those tools in the story from the model: I derive the need for those tools in the model from the story. It simply wouldn't make sense to be blocked from attempting that action on the grounds that my character doesn't have lock-picks: I want to have a scene where I pick that lock, therefore my character must be in a position to do so, therefore we can retroactively insert the required elements into the model.
This isn't a black & white world and the model-first and the story-first styles don't represent absolute approaches to role-playing: they are the points at either end of an axis of play styles, which we can move along within the body of any given game. One example that sticks in my mind comes from an old school Battlestar Galactica game: the players created their ace pilot characters, picked skills, equipped them, climbed into their Vipers for their first patrol... and slammed nose-first into the launch bay doors, because the GM ruled that they had neglected to send the request to the launch deck for the doors to be opened.
It's a hard way of learning this, but clearly the GM was playing with a more model-first mindset than the PCs, who were probably also predominantly of the model-first school, but expected it to be story-first in basic, common sense situations like doing things their trained, skilled ace pilots would know to do automatically. We all come to the game with expectations of how specific we need to be about the actions of the characters, whether we are PCs or GMs: when those expectations don't mesh perfectly, we get frustrations, hopefully not as extreme as the example above, but there nonetheless. At some point, we accept that the model constrains what the characters can do: I can only try to pick the lock, I can't burn through it with my laser eyes because the model doesn't contain those kind of powers. We also want to get on with things though and not be made to got through an infinite regress of modelling before anything is permitted to happen within the story: it's enough to establish that lock-picks are available and that the character can acquire them, we don't need to account for every second taken and every penny spent in doing so.
There will always be games that tend towards one end or another on the axis of model-first to story-first and we'll all have preferences for where we like to be on the spectrum within given situations: I'm strongly story-first, but I'll make model-first objections if the story is being pushed beyond what I find plausible ("And where did you get 12 sticks of dynamite from, exactly?") I know a number of players who are at the opposite end of the spectrum from me, who view a precisely modelled character in a precisely modelled situation as a big, exciting puzzle box with moving parts (that have sharp bits on) for them to overcome, but I'v also seen them object to content on the good-old grounds of "Can anyone tell me why we're doing this?"
The model has to function for the story to be plausible; the story has to be plausible for the model to function. Neither has primacy and both are moving targets to aim for with varying accuracy as we play within the range of styles we like the most.