I was just discussing Burning Wheel with a friend who had heard of it and wondered what was different.
I enjoy multiple FRPGs. But if I had to choose a favourite, it would be Burning Wheel.
I've only played it a few times, but it really does depend on your definitions of who your character is, and proceeds to put them through a wringer. Everything you do is based on that character's beliefs (really their BITS if I'm remembering the term correctly).
Also Relationships, at least when I'm GMing. Though these will often be bound up with Beliefs.
A GM sets the tone for the game, asks you engage with it, but the game does this as well (unless the GM fights against it).
The players too. My Torchbearer 2e has a comic aspect to it, and that has 100% come from the players, not me: the Elven Dreamwalker Fea-bella; the Dwarven Outcast Golin, who was raised in a cult dedicated to explosives; Telemere the Elven Ranger, who seemed serious at first but most recently was - as narrated by Telemere's player, to explain what had happened to him during a couple of missed sessions - capture by Gnolls, put into a barrel to be sold up-river as cured meat, but not fully pickled (insufficient salt in the brine) such that, when the Dwarves opened the barrel to get out their meat, out stepped Telemere.
Torchbearer does have something about it that invites this comedy - I've posted before that it can do The Hobbit, and probably also the Silmarillion, but not LotR - but I wouldn't have introduced it if left to my own devices. (I'm too po-faced!)
To have only one approach for roleplaying would be like playing as if you're in Burning Wheel with the Paranoia rules.
Or another analogy I've seen - it would be like turning up to a canasta game and starting to bid for tricks that one will take.
Rummy, whist, poker, etc - these are all card games, but how they are played, what counts as a good hand and good play, etc, varies between them.
The same for RPGs: Burning Wheel, Torchbearer and AD&D all use the core idea that one participant presents an imagined situation, and the other participants "navigate"/"resolve" the situation by saying things about what a particular protagonists in that situation does. But the rules and conventions around
how situations are established,
what the content of the situations is,
what counts as appropriate action declaration by a player, etc - these are different from game to game.