Yeah, a partial hit or a miss allows the MC to make some kind of move.
However, the move doesn't have to be an obvious result. The "fire" that you're referring to, is whether or not you pull off whatever it is you are going to do. If you fail or partially hit that roll, then the MC can make a move stemming from this, that complicates the situation, and the move should be supported by what makes sense in game. With sneaking, the Fire isn't necessarily getting caught. It can be a bunch of things.
For example, if JC is sneaking by Parcher and his cannibals (grotesque: Cannibal), a miss means that I can do one of the moves, and it can take a variety of forms. Here's a few examples:
The cannibals cut off JC's avenue of escape (Putting him into a spot).
The cannibals drag JC's girl Amy into their camp and begin slathering her with barbecue sauce (Capture someone).
JC is distracted by the sound of an intense gunfire as it echoes from somewhere up near the Holding "Six Blades" (Announce off-Screen Badness).
JC sees that the cannibals have a rough map of the nearby Holding "Six Blades", and are discussing weak points they can take advantage of. (Announce future badness)
And that's just from the standard moves. From the Grotesque moves, there's a choice of more moves I can make:
JC stumbles into the garbage pit, filled with the gruesome remains of the people eaten by the cannibals. (display the nature of the world it inhabits)
JC is surprised by a skulking cannibal, who stabs at his back with a steak knife. (Attack someone from behind or otherwise by stealth)
JC is discovered by Parcher's head cook, but told he can leave without further discovery if he "Just takes a bite from the main course, let me know if the meat's nice and tender". (Offer something to someone, with stings attached)
Again, there's lots of possible consequences, and they all stem from the moves available. Just remember to scale the awfulness of the move appropriately, a partial hit means a partial success. Sometimes the urge is to treat a partial hit like a full on failure, and that shouldn't be the case.