I also found Baker's writing to be too deeply into the weeds of Forge-speak to grasp on first 3 reads. So I got help. (From Luke Crane and Thor Olavsruud)...
Still haven't (and won't) play nor run AW - I don't care for the setting elements included. But one particular PBTA game has my interest (MASHed).
The most important element that's different is the way actions happen. Players narrate until...
- they narrate doing something covered by a move
- they pass off to another player
If no one is ready to narrate, the GM then does a move. Usually not one of the majorly unpleasant ones.
Moves are always thematic to the ruleset's setting tropes; they're about bringing the pain when you don't get full success. They're the only actions which get rolled; others are all in "say yes" mode.
Moves have 3 outcomes: Success, partial success, or failure. Partial may be literal partial, or may be success with complication. Whichever way, it's over, move on
If you narrate doing something that's within scope for a move, narration stops, and the dice get rolled.