The Big Model recognizes three categories of arrows, or intentions. A lot of people think it categorizes types of gamers - it doesn't, people play for different reasons at different times (but some like this or that way better, true). A lot of people think it categorizes games - it doesn't (they're just boxes of bricks, but some with intentions behind them, true).
The categories of arrows categorize play, over a period of time, as it is informed by those arrows. As far as arrows are concerned I can buy a lego house set, but if I use it to build a rube-goldberg machine, it's appropriate to say that my play in this instance is of the "rube-goldberg type", regardless of the set I'm using. It would be also wrong to categorize me as a "rube goldberg player" since on a different day I might be building a tower or a working model of a car engine. No, it's not about game sets or players it's about play. Actual play. From saying "let's play" and sitting down to rolling the dice. And it's about the activity, or continuity of play, and not an isolated moment of it.
So if you observe people at play (and not people as individuals, and not the individual sets of rules), and if you observe them over time, you'll usually see them prioritize - so says the big model - one of the three things:
-using roleplaying to create narrative with thematic content or "Story Now"
-using roleplaying to solve problems and overcome challenges or "Step on Up"
-using roleplaying to celebrate a certain portion of their shared imagination "Right to Dream"
Prioritizing means that one intention takes precedence over the other, the others are sidelined, less important, not the point of play, not the object of interest. It doesn't mean they doesn't exist it the game in some form, they're simply not something we care about.
Story in Story Now means taking a motivated character through series of unsustainable situations, which necessarily creates change (in the character and the world) which has a thematic value. Now means we're doing it live, at the table, and that theme is not determined before play, or retrofitted afterwards or nonexistent.
For example: "The Dark Wizard runs down the right tunnel to kill the king while his henchman grabs your fiance and runs down the left tunnel. What do you do?". The character can not not make a choice that would mean something (for example: what's more important loyalty or love?), it's also not really a tactical or strategic choice, which could be dealt with as a challenge. And since it puts things at stake, with inevitable consequences and change, it often goes against pure celebration (for example: whatever I chose it would kinda break my conception of my character as a big damn hero who saves the day and gets the girl)
Stepping on Up means stepping on up to the challenge. It's a display of skill, it's about joy in (friendly) conflict. It's like group sports or bar games with friends for example.We want to play hard, trashtalk, make the best choices for winning, cheer and high-five when we're winning, grit our teeth and swear revenge when things go bad.
For example: "Do I attack the fire elemental with ice magic (which is smart) or fire magic (because that's "what my character would do")?" If we're playing for victory, for display of skill, I need to do the smart thing, within the constraints of the fictional situation. It's not a primarily a moral choice (although those can provide elements of the challenge) and it's not really a celebration of some aspect of the fiction (since my character as conceived would use fire).
Right in Right to Dream means that affirming the "dreams" of the players (GM included) takes precedence over other concerns. Dream means the fictional world we want to immerse ourselves into, the identity of our character (or our own), the details, the setting. We are interested in "getting it right", whatever "it" is. Our priority is staying true to the concepts and standards that we have set.
For example: When playing in an official setting we try to stay true to the themes, tropes, genre etc. as presented in the original work.
You can see that those same situations can almost always be turned around. The choice between loyalty and love could be made in the context of a greater strategy (for example, go after the fiance because the henchman has the key to the villain's defeat - no moral pondering involved). The choice between fire and ice could be made a thematic quandary (for example: I am sworn to a god of fire, with consequences - is using ice to save a friend worth my god's ire: friendship or creed?). We can play in an official setting but only use it as a backdrop for challenges or use it as a "what if" springboard of thematic exploration that isn't concerned with fidelity to the original. It depends what kind of aim we're approaching play with.
Aims can also disrupt one another. If my character's concept is "loyalty above all", and I'm playing Right to Dream and the GM is playing Story Now and puts me in a situation where my loyalty is at stake (where I must make a thematic choice), I have every reason to feel unhappy or betrayed about it. I may enjoy the portrayal of my character in a difficult situation, enjoy experiencing the internal conflict, but deep down I'm not really expecting to betray my loyalty. I expect to keep it without consequence, because that's my dream and I expect to have a right to it. This is why in the second post I stressed that arrows were to be understood as a collective, group intention.
So that's the whole of the Big Model:
1. Nested boxes, that have these things in them: [Combination of Real People[Imaginary Stuff Shared Among Them[Procedures[Play]]]. Lots of possible elements and combinations.
2. An arrow, the intention that drives these people to play together and informs the choice of elements from the boxes, from organizing a session down to rolling an attack.
3. Intention to use play to: create thematic narrative, be challenged or use play to realize fantasies. Prioritized over a period of time, collectively.