See previous discussions on this (topic #3235 and topic #3939).
Frankly, Bloodletter's comment in the former topic is close to what I'm thinking on "arm holding" and "arm grab" currently: the latter only when it's clearly more forceful. It may be worth keeping them separate.
I don't think implicating arm_hug to arm_grab makes sense to me. The character may have their arms wrapped around another's arm without grabbing it with their hands.