how a character feels or reacts to outside stimuli defines who that character is as a (fictional) person. By contrast, whether or not a character has been in a situation where they learned a particular factoid about the campaign setting (and/or whether or not they remember that factoid) does not define who that character is as a (fictional) person.
So a mechanic that tells you how your character feels or reacts I see as redefining a character in a way that a mechanic that tells you if your character knows a particular bit of lore does not.
I'll put to one side possible counter-examples to your account of what defines a character (eg perhaps a character is defined as
always knowing every last scrap of trivia).
As was posted
way upthread, one function of a game system like Burning Wheel (or even Prince Valiant, though it's less intense) is to put pressure on
who the character is, including in the sense you've defined that.
I quoted the relevant text from the Burning Wheel rulebook; here it is again (p 9 of Gold; Revised is the same):
In the game, players take on the roles of characters inspired by history and works of fantasy fiction. These characters are a list of abilities rated with numbers and a list of player-determined priorities [ie Relationships, Beliefs, Instincts, some traits, etc]. The synergy of inspiration, imagination, numbers and priorities is the most fundamental element of Burning Wheel. Expressing these numbers and priorities within situations presented by the game master (GM) is what the game is all about. . . .
There are consequences to your choices in this game. They range from the very black and white, "If I engage in this duel, my character might die," to the more complex, "If my character undertakes this task, he'll be changed, and I don't know exactly how." Recognizing that the system enforces these choices will help you navigate play. I always encourage players to think before they test their characters. Are you prepared to accept the consequences of your actions?
The in-game consequences of the players' decisions are described in this rulebook. The moral ramifications are left to you.
I think it's obvious that this is presenting an approach to RPGing, to the place of the character in the fiction, and to the player's relationship to their PC, which is pretty different from default D&D. I posted this example/illustration not far upthread:
Upthread I've posted (inter alia) an account of my PC's prayer to restore vigour to his mother. The immediate trigger for this, in play, was that the GM was about to start a Duel of Wits in which Xanthippe (Thurgon's mother) was going to implore Thurgon (my PC) not to leave her alone again. The prayer had weight in itself, because (mechanically) is was slightly more likely to fail than to succeed and (in the fiction) having it go unheard in such a moment of crisis would have been devastating for Thurgon (and there are mechanical ways, too, to follow through on that). But it also had weight because of what would happen if it failed - I (as Thurgon) would be drawn into an argument about my past and future behaviour (I was not going to walk out on my mother, when this was the first time I'd seen here in five years!) and there was no guarantee I would win it! (Thurgon is not terrible at social actions but not great at them either. And Aramina probably would have helped Thurgon, but only by saying cruel things to Xanthippe, which would have been hard too!)
D&D characters are not expected to change. (I quoted some AD&D text upthread which emphasises the importance of
not changing, especially in relation to alignment.)
In other RPGs this is not necessarily the case: characters
are expected to change, or to be revealed, in ways that outstrip any single participant's authorial control. (Much as, in D&D, combat is normally expected to unfold in ways that outstrip any single participant's authorial control - hence controversies around "fudging".)
In aesthetic terms, this can be looked at both "internally" and "externally".
Internally, it may help produce the type of emotionally laden play that
@Campbell and I have tried to articulate upthread.
Externally, it may produce a shared fiction that has a higher degree of drama and thematic content, compared to an adventure story in which the interest and excitement flows primarily from the thrilling action rather than the inner struggles of the protagonists.