I think @soviet's reply to this post was pretty solid!How different can the fundamental play loops be, though?
I mean, when everything else is stripped away in what RPG doesn't the play loop boil down to:
1. Player(s) say what their PC(s) (are trying to) do next, as an action declaration or similar based on the current state of fiction
2. The game's resolution engine processes that declaration and generates a result
3. Someone (usually, but not necessarily always, a GM or equivalent) translates that result into a narration of what, if any, observable changes have occurred in the state of fiction as a result of that (attempted) action
4. Go to 1.
That different games have and use widely different resolution engines doesn't affect this fundamental play loop; and most of these discussions are really only about variants of resolution engines and-or different philosophies or principles involved in steps 1 and-or 3.
But here's mine.
First, as soviet asked and as @chaochou so often emphasises, who established the current state of the fiction? And to add to that, who established what it is that the PC wants? Is the player following a GM-authored hook, or is the player establishing their own goal for their PC?
Second, the game's resolution engine is an abstract object. Who actually "processes the declaration" and generates a result? Suppose that a player has their PC call on a god for aid with whatever they're doing: which participant gets to decide if that prayer is answered? Just as one example, Agon answers this question rather differently from Gygax's AD&D.
Third, the drawing of a distinction between "generating a result from the resolution engine" and "translating that result into narration" is not common to all RPGs. It doesn't obtain in BW when the GM "says 'yes'"; nor if the player rolls the dice and succeeds. It doesn't obtain in AW if a player's action declaration doesn't trigger a player-side move.
Fourth, the idea that narration is of an "observable change in the state of the fiction" appears to rule out a range of possible consequences relating to ideas and emotions.
Fifth, after narration of consequences and before calling for new action declarations there may be the introduction of new fiction eg as the result of a wandering monster check; or because the GM decides to spice things up; or in some other way. How that sort of thing is done is a big part of any RPG experience.
I'm sure there's more that could be said.