That side steps my question. Drives from it!? The underlined part - F > S > F. Where the 'S' is DW Hack & Slash. What about the mechanic drives the following F?
Well, this is where DW/PbtA 'holds together' as a system quite well. ANY move will demand a return to the fiction. I mean, suppose an Orc approaches you with hostile intent, and you declare that you're going to fight him, and pull out your sword. This is about as cut-and-dried as it gets, the GM could reasonably just rule that you've invoked an H&S move. So, what are the possibilities here? You could roll 10+ and simply pig-stick the orc, forgoing the extra 1d6 damage option. You could roll 7-9, in which case you simply take damage in return for dealing it. 6- subjects you to some sort of GM Hard Move.
So, 10+ you MIGHT simply damage the bad guy and there's no other real fictional consequences. Note that in DW hit points are a very limited resource and even high level PCs don't have large stacks of them, so the fictional outcome of damage is MUCH more easily established than for D&D! That is, any blow that does 10 damage to ANYTHING seriously injured it! Likewise if a monster dishes out 10 damage, the result is pretty serious, and can be reliably narrated as such. There is MUCH LESS need for the Gygaxian equivocation about hit points that are 'luck' and whatnot! So you got a 10+, and assuming your opponent isn't killed outright by the resulting damage, the GM can narrate the result predictably in the fiction. The GM is also free to impose a soft move at that point, which could be anything, but will HAVE to be fiction-based, as there's no mechanical basis for initiating moves in DW. (IE "the orc takes your blow and attempts to push past you to get to the wizard!").
On a 7-9 there's likewise wound fiction for each side, and again the GM COULD come out with a soft move.
On a 6- the GM MUST respond with a hard move. This is going to be, necessarily rooted in the fiction, there are no mechanics that can simply generate such a thing. The most mundane answer would be something like "The orc takes a big swing at you with his axe and you take N damage!" Honestly, it could be anything, as long as it hurts and it follows from the H&S move and its fiction.
Now, the above example is about as cut-n-dried as it can ever get in DW. I'd note that there is NO TURN STRUCTURE, so once this interaction happens, the other players and the GM are going to be going back into the fiction and generating new moves. Maybe at this point the wizard pipes up with "I cast a magic missile at the Orc!" or something like that. This is again about as clear cut as it gets in terms of move generation, and admittedly the fiction part of it is more in terms of the wizard player adding his input at this point (again no mechanic dictates this, there's no initiative order or anything) but it is true that casting a spell is pretty mechanical in terms of how it works, at least up to a point.
But, really, in actual play IME, straight up combats rarely get very cut-n-dried. If you want to WIN and you don't want to just get chewed by every monster, you better learn to invent some tactics and bring some more fiction into play. For example the Dwarf above, his player could say "What do I know about Orcs that might help me here?" and all of a sudden he's spouting some nasty curse in the orc's face which makes it recklessly attack him and gives him some forward! This is the sort of thing that DW does, by its very design. It brings this stuff out.
Now, contrast with 4e, which can get pretty 'fictional' in some styles of play. Maybe a player pulls a Monster Knowledge or some kind of Lore check and then utilizes it to invoke a skill (Minor Action, spout a curse at the orc which gives you a +1 on your attack). This kind of thing is often cued via some keywords, or the easily invoked structure of the conditions (IE I toss a flask of oil in the troll's face, and it reels back, fearing the fire which comes next!). 4e reduces the impedance of these kinds of things a lot by keywording things heavily and providing ready-made conditions and things like forced movement to represent them, as
@pemerton pointed out earlier.
Anyway, in terms of DW it is VERY HARD to get into anything resembling a D&D-esque mechanics-first combat loop. There MIGHT be a pair of moves traded between GM and player that could be colored that way now and then, but the game simply doesn't produce things like several rounds of combat in which everything is pure mechanics with only incidental narration for color, which 4e or 5e can easily do.