"Play to find out" is something I associate first and foremost with Apocalypse World. But I would say that BW is broadly similar in its aspiration, stated in that abstract way.
When we get down into the technical nitty-gritty, BW is different from AW. It is based around the scene as the basic unit of play, and around "intent and task", "say 'yes' or roll the dice" and "let it ride" as the core principles of action resolution. (Whereas AW uses player-side moves together with "if you do it, you do it".)
The family of games that BW belongs to (in rough chronological order) is Prince Valiant, Maelstrom Storytelling, HeroWars/Quest, In A Wicked Age, Dogs in the Vineyard and (at least as I read an play it) 4e D&D. (And also BW's own offshoots, like Mouse Guard and Torchbearer.) Some Ron Edwards games (eg Sorcerer) probably belong in there too, but I don't know them well enough to be confident about that.
What these games have in common is the scene as the basic unit of play, and
intent and its connection to clear stakes (whether expressly articulated, or implicit in the scene) as the crux for the resolution of action declarations: if the player succeeds, their PC realises their intent; if the player fails, the GM narrates what happens and is expected to do so having primary regard to the PC's failure to realise their intent. This is what escalates the stakes, and thus creates rising action.
The way that Burning Wheel does scene framing is this (I'm quoting from pp 9-11 of Gold Revised, which has slightly clearer wording than Revised):
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. . . . 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. . .
Burning Wheel . . . is inherently a social game. The players interact with one another to come to decisions and have the characters undertake actions.
One of you takes on the role of the game master. The GM is responsible for challenging the players. . . . Everyone else plays a protagonist in the story. . . . The GM present the players with problems based on the players' priorities. The players use their characters' abilities to overcome these obstacles. To do this, dice are rolled and the results are interpreted using the rules presented in this book.
So the players build their PCs, which include player-authored priorities (these are expressed in a range of ways, including as Beliefs, Instincts, Traits, Relationships, Affiliations and Reputations). The GM, having regard to those priorities, frames scenes (or "presents situations") which pose problems/obstacles
in light of those priorities. The players then declare actions. These are resolved via the principles/techniques I mentioned above (intent + task; say 'yes' or roll the dice; let it ride). And the upshot is then worked out, feeding into a new situation. Because of the role of intent in establishing consequences (if the player succeeds, they get their intent; if the player fails, the GM narrates a consequence that includes the player not getting their intent), whatever the upshot is, it will pertain in some fashion to the player priorities.
The difference from some other approaches to RPGing in which the GM tells the players where the PCs are, and what is happening, is that
what is happening bears directly upon the player-determined priorities. To support this, the BW rulebooks have extensive discussion on how players and GM can work together, at the outset of a game, to establish an initial situation and background in which those player-determined priorities can be expressed and put under pressure. In functional terms, this is similar to the first session in AW.