I think that this attempt to describe particular mechanics, or other processes of play, in rather abstract structural terms, with an expectation that doing so will then carve some significant boundaries of preferences for play, is hopeless.
I'm going to use a post of yours not too far upthread to elaborate my point:
There is no structural difference between a die roll that establishes in the past, an event occurred whereby I learned that Orcs of the Broken Bone worship Baghtru and a dice roll that establishes in the past, an event occurred whereby I learned that Evard's tower was in such-and-such a place.
Nor is there any structural difference between those sorts of rolls, and one that establishes that in the past, an event occurred whereby Evard's tower came to be in such-and-such a place.
Some posters might think there is a structural difference, because the knowledge involves the PC and the tower involves a NPC, but I think that thought won't be defensible under scrutiny. The PC having learned something implicates NPCs - there was an NPC teacher present, for instance, telling the PC <whatever it is that the PC learned>. And the tower one implicates the PC, as the presence of the tower is a causal factor in the PC's knowledge of it.
I don't think that trying to draw the distinction in terms of topic or substance will work either. It's true that the knowledge rolls focus on the topic of the PC having learned something in the past, while the tower roll focuses on the topic of a tower having been built in the past. But given that the proposition A knows that X entails X, the contrast breaks down under even modest analysis: if my PC accurately recalls some fact about Orcish cult practices, that entails a whole lot of setting stuff about Orcs and their cults.
The real issue of preference, as best I can tell, is about which participant - player or GM - gets to establish or "own" which bits of the fiction. So rather than worrying about "narrative" mechanics or "diegetic" mechanics, or even "metagame" mechanics, to me it would make more sense to directly talk about that real issue.
One obstacle to doing so is that it collides fairly immediately with the assertion that "The player decides what their PC thinks and feels". That statement, while it may be true as a generality, is literally false of a game in which (i) the PC is not particularly stupid and hence tends to believe true things, and (ii) the PC, given their background and training, probably believes some true things about Orcish cult practices, and (iii) the GM is the participant who is entitled to establish Orcs and their cults as elements of the fiction.
The reason for including (i) is to rule out the (surprisingly common) retort that the player is freed to have their PC believe false or outlandish things, but the GM will decide whether or not they are true. Once (i) is included, the interplay of (ii) and (iii) fairly clearly entail that it is the GM who will decide what the character whose player succeeds on a History/Religion/whatever check wil believe about Orcs and their cults.
Because of the weirdly shibbolethic status of "The player decides what their PC thinks and feels" I don't expect this post to generate wide uptake in this thread. Nevertheless, I think it explains why the attempt to analyse RPGing preferences in terms of abstract structural labels is not a very profitable one.
