First is the distinction between the moves "Shut someone down" and "Lash out physically".
"Shut someone down" is anything you do to arrest or emotionally hurt someone. Usually this is done with harsh words, but the rules specifically state that is also includes physical attacks that aren't intended to cause major bodily harm -- the example given is shoving someone against a locker.
"Lash out physically" is for when you *are* trying to cause major injury to someone. The examples given in the text is biting someone with wolf fangs or shoving someone off a balcony.
It's a major, major escalation from "Shut someone down".
And imo, the fact that the rules for each move implicitly construct the possibility of this as escalation is really, really cool.
One of the options for partial success roll on Lash Out Physically is that instead of doing one (or maybe two) Harm out of a fatal four, the MC (game architect/facilitator) decides how much Harm is done.
A real possibility of a not-quite-as-intended attack is that you hurt the target far worse than intended. Again, the Lash Out Physically move is serious business.
I think the purpose of this -- and of it being pretty visible on the character sheet -- is less because any particular move is important and more to communicate "hey, this is a game where having sex with folks is a real and encouraged thing."
Anyway, the rules for Monsterhearts are pretty short but do a really impressive job of guiding you towards certain modes of play.
You can get it here, and hey, it's on sale!
https://www.drivethrurpg.com/product/212511/Monsterhearts-2
It also, like the Lash Out Physically move, communicates "This is a thing you can do but the consequences may be serious and unpredictable." This builds on the game's themes.