Exactly! Great summary. The forearm variants can feel more deliberately effortful, depending on the pick path you are requesting. If you’re trying to move pickup-parallel, you’re using more flextension. If you’re trying to move more diagonally, in line with the forearm’s axis of rotation, then you’ll have more arm movement and less flextension. These have different feels so the movements make themselves known in that way.
But in the case of the wrist-only movements, in my experience, the components are not things you think about or try to “do” deliberately. In other words, I’m not thinking “pickslanting movement with a thing tacked onto it”. I’m putting the arm in a particular setup and making pickstrokes. It just feels like side to side movement.