In this thread there has been reference by more than one poster (most recently
@prabe just upthread) to a "spectrum" which has sandboxes at one end.
I think this is an unhelpful and even misleading confusion. It makes discussion of authority over the fiction harder than it needs to be.
So just to be clear: there is a spectrum on which colours lie - I'm not any sort of expert, and tend to suck both as visual artist and critic, but in my mind I can conjure up a spectrum that runs from yellow through orange to red.
Some spectrums are more metaphorical than literal: we might say that there is a metaphorical spectrum from square through pentagon through hexagon through . . . through chiliagon . . . all the way to a circle.
I personally struggle to think of even a metaphorical spectrum that has a triangle at one end and a square at the other.
And cars, trucks, and bicycles are all land vehicles but I don't think they sit on a spectrum at all.
So:
A
sandbox involves predominant, even exclusive, GM authority over
setting and
backstory. (Maybe players contribute some backstory at PC gen, which they and the GM weave into the GM's notes about the setting.)
Many of the GM's setting elements - lairs, prisons, political factions, etc - have latent
situations in them.
The players "activate" these situations by declaring the appropriate actions - eg that their PCs
cross the hills to find the dragon cave or that their PCs
talk to the mayor to try and secure her support in their attempt to overthrow the Baron.
So the players and the GM share situational authority, in the asymmetric fashion just described.
As far as action resolution is concerned, the GM - if they are not going to be self-defeating - has to be generous and permissive in adjudicating the "activating" actions. How other actions are adjudicated, and whether "Let it Ride" applies, is a different thing. I can certainly conceive of a GM who is very protective of his/her sandbox and so makes sure that player-declared actions don't really do much to
change the setting (ie Let it Ride does not apply, and the GM manipulates the background fiction to negate possible significant consequences of PC actions).
Now consider the typical
"linear" adventure - in D&D terms there are many of these, but Speaker in Dreams (a 3E module) is as good an example as any. In these adventures the GM also exercises backstory authority. The GM also exercises situational authority. And - related to this - whereas the sandbox GM should be very permissive in adjudication of "situation activating" actions, the GM of the linear adventure wants to discourage any such actions which might activate situations that have not already been planned/prepared for - either by express metagame requests to the players, or by using in-fiction techniques to discourage them (eg lots of "There be dragons" signposting), or by using adjudication techniques to block them (such as fiat declarations of failure; stuff like anti-teleport zones is probably on the line between in-fiction and adjudication-based techniques). And in a linear adventure Let it Ride
can't apply, because the GM is committed to presenting the upcoming situations whatever the PCs' actions (subject to extreme unavoidable changes in the fiction like detonating a bomb - those actions also risk detonating a metaphorical bomb at the gaming table!).
So we can already see that there is no "spectrum" here, just different allocations of authority.
Now consider (say) Apocalypse World. The backstory authority is shared, as part of PC build. The GM exercises situational authority, exercised in accordance with the principles of the game. These include
ask questions and build on the answers, which can mean taking significant suggestions and input on both backstory and situation during the course of play (eg the GM might ask player X,
so why is Isle so mad at you? and then the player has to make up some appropriate bit of backstory which also helps inform the character of the current situation). The integrity of action resolution in AW is of course sacrosanct.
Again, no spectrum. Just different allocations of authority.
EDIT: I've just read
@Composer99's post not too far upthread. I'm curious how much Composer99 thinks our descriptions of "linear adventure" differ - eg am I describing only a degenerate case? That wasn't my intention, and I don't think I am, but maybe I've missed something!