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.
Simply in the definition of these moves, the game communicates that 1, serious physical violence is an option you have, but also that 2, you have to really mean it.
It also gives you the vocabulary to use lower-level physical attacks *without* attempting to cause bodily harm.
The other really interesting place this happens in game is with the Sex Move.
All characters have a Sex Move written on your sheet. Basically, when you have sex with someone, something happens to one or both of you. It can be a good, bad, or mixed thing depending on the Skin (character class/archetype).
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
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.