Maybe it's "Authored" vs. "Emergent"

[Cheesegear]

That same scene can happen in both types of game or anywhere on the continuum in between.

Okay.

Based on the narrative, their character, party dynamics and what the player wants to get out of the game; A player uses their agency in a specific way.

The DM knew that that player - or entire party - would use said agency in that specific way, and is already prepared for that eventuality (i.e; I knew you would do that, lol). Or maybe starts authoring new content based on how the player used their agency, so that when next session happens, they're still on the author's tracks...Just not the same tracks they were on last session. 7 days is a pretty long time. You can come up with something between sessions.

The player - or party - used their agency...
In the exact way that the DM knew they would, and is already prepared.

I don't know how else to explain it except as a train line map: You're going to get on a train, the DM just don't know which train you're going to pick. But he has the trains, ready to go, you just have to get on one. And you can take that analogy all the way down to the encounter-level; There are four major train-lines out of this encounter (FRST). I have the trains ready to go. If you want to fight, let's go down that line. If you want to stealth around them, let's do that one. Whatever you pick, I'm ready. How 'bout you? There are maybe one or two minor train lines out of the encounter, but they aren't really marked on the train line map, and are more of a 'secret menu' item that you can get on if you're clever...Maybe.
Then of course there's just acting irrationally. We'll try and avoid that, yes?

Did that help?

Yes but probably not in the way you think. Describing it as a continuum is probably the worst answer you could give, because that's basically the only answer I don't want. But knowing that that is the answer, probably means that I should've left the thread a long, long time ago, and labels are a hindrance, not a help.

However that is vague enough and zoomed in enough to be unrelated to the topic.

We're going back to the OP. Try and follow my logic:

Authored
There can be optional branches, there can be some shuffling of what order things are done in, etc. But the key is that all the things that are done, all of the situations handled are things that were predetermined.

This doesn't mean that authored games have no agency, though they have very limited or no agency in specific areas - usually in terms of what specific encounters/scenes happen. Sure, you can change some aspects of hte result, or you can have side-effects, often significant, on the world, but you're really going to mostly go along the same path as others

This has advantages! Since the GM knows what the players are going to be doing, the GM can prep very cool, detailed, prep-intensive things for the players to do - custom actions, cool terrain, super balanced encounters, etc.

Emergent
Sure, there can be some initial elements, but what the players do is fundamentally unknown, and how the world changes in response to their actions is also fundamentally unknown.

But fans of emergent games want different things - they want their decisions to matter. They want the game to take on a different shape than it would have if they had made other choices. They want to be able to solve the problems their own way. They want to do things that the GM didn't plan for, and they want to make that take the "story"/game in a way that the GM could not have predicted.

...You can see where there's overlap, can't you? There's a fuzzy middle ground where the players can do what they want, but the GM already knows what they're going to do, based on whatever information the GM has about their players and characters.

What about this situation that I - and I'm certain a lot of other people, too - do? Where does this very normal situation fit into this dichotomy?