I can see this. And if the topic of the thread is drifting in the direction you set out here, that's fine with me.I think that the whole "GM's notes" thing can be simplified a bit into just "GM decides." This mode of play is where the GM is the arbiter of what happens in the fiction, so play occurs according to the GM's understanding of the game world and the fiction.
Now, within this scope, there's shades of difference, one of which is very much dependent on the GM's notes, or, rather, that the GM has pre-established in a largely fixed way a large amount of the game fiction. The play is then to determine what is in the GM's pre-conception of the game fiction. This is where Skilled Play a la Moldvay dungeon crawls situates itself. It's still under the auspice of GM Decides, but it's a subset.
Another version of this is where the GM has few or almost no notes, but is still the source of how things come about in play. This is what's usually referred to as improv or ad-lib play by posters unfamiliar with systems built to generate content during play. This is what a D&D game with a "loosey-goosey" GM looks like.
I had started the thread about GM's notes rather than GM decides because the two don't overlap completely (in logic, at least; if we surveyed actual play at actual tables the degree of overlap is probably quite high). The notes in a PbtA-ish system, for instance, provide a resource for GM moves in various contexts but I'm pretty sure you're not wanting to include those within the scope of GM decides. (And I would agree with you in that respect.)
The "loosey-goosey" GMing is what Lewis Pulsipher was pretty critical of back in the day. He distinguished "realism" RPGing (C&S was the example he pointed to; some approaches to RQ are probably similar; we might now call that process-simulations) from "wargame" RPGing (classic skilled-play D&D is the exemplar) from "lottery" RPGing (a lot of T&T can look like this) from "GM as novelist/storyteller" RPGing (his least favourite, I think, and what you're calling "loose goosey"). His reason for favouring wargame play is that it maximises the roll of player skill. When surveying the state of the art when he was writing, I think he was correct about the descriptive part of that claim, ie that player skill is of little importance in lottery and loose-goosey play, and of reduced importance in process-sim play because the processes take over.
I think there are innovations in RPG technique since the early 80s that change some of the parameters, though, as you point to in your post: as well as systems built to generate content during play I would mention closed-scene resolution, and also a richer understanding of how narration can be structured around action declaration both at the point of framing and when establishing consequences.
Yes.To contrast "GM Decides" you have systems where the GM is tightly constrained, usually by having no pre-conception of the fiction, only the fiction as introduced, and with rules that state that actions cannot be blocked, only allowed to succeed or be challenged with the mechanics. They also have mechanical systems that allow for both player and GM input, and tight constraints on the outcomes. These are the Burning Wheel, PbtA, FitD style games.
I have no Fate experience, but on rpg.net I have seen discussions which say that it can be used for GM-curated play in a way that Burning Wheel just can't.Somewhere in the middle of both of these are systems that can swing either way, depending on the GM. FATE, despite my not grasping how it can be a GM decides game and work at all, is apparently one given play reports. D&D 4e is another. From how @pemerton describes Traveler, I'd say it fits as well.
Classic Traveller is a very interesting design because it has the baroque subsystems one associates with process-sim, but mostly these end up being little pockets of closed scene resolution. It has resources for generating content via random rolls which - because of the closed scene features of the subsystems - can be used in real time during play and will work smoothly in a way that is trickier (in my experience) when doing Appendix A random dungeoneering. To try and give a simple explanation, Appendix A can fairly easily produce "Why did the Orcs in this room we just rolled not respond when we trashed the fire beetles in that room next door that we rolled up first, given that there is only a door and not even a corridor between the two rooms?" and similar sorts of oddities that push against the coherence of the fiction. Whereas the basic conceits of Traveller together with the ways its very subsystems unfold and interact mean that random content generation is (or at least seems, in my experience) not to produce very much of this.
A lot has been posted over the years about 4e D&D so I won't add anything to that here.