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

[Tanarii]

In theory an emergent GM could predict what the players would do and prep accordingly while letting them make decisions.

In practice, I have doubts. Once you start designing something, it's kind of second nature to prep the path to it as well. It's also incredibly easy to start making other things subtly harder or putting up resistance, so when players see that, and see the prepped path, they start just looking for the path.

I'm not saying it's impossible - but I don't think I've ever seen it executed on well. It's also the kind of thing that from the DM's side can be hard to detect, since how do you know if you predicted players, or steered them onto that path? A lot of times players expect a path, and look for the path (see examples in this thread and others). From the GM's PoV, that kind of implicit participationism looks a lot like correctly guessing what the players will do.

This is why in "sandbox" emergent play it's traditionally location prepping, with factions prepping later on coming into the fore. Of course, a lot of location prepping for sandboxes traditionally also includes just-in-time events triggered by PCs arriving on the scene, which probably blurs the line into authored (at any given event location). Even if not, if it's not also faction-based, there's also a good chance the locations are siloed and reactive, not proactive. But location prepping gives PCs places to go explore, which can later on be repopulated with new denizens if the current ones are wiped out. And campaign events emerges as gameplay happens and the locations are "unlocked", causing any denizens/factions (if they survive) to now be more proactive parts of the campaign setting, showing up in other locations and potentially even doing things like launching plots/invasions against the PCs settlement(s).

Of course in a true sandbox campaign, there are multiple groups of players and PCs, and their actions aren't only affecting their future experience in the campaign world, they're also affecting other groups of players and PCs.