Still sounds like a badly chosen name to me. Calling a category "weapon attack" when not all attacks within it are attacks with weapons makes it wide open to misinterpretation, especially when in some cases it's relevant whether a weapon is used or not. The fact that it took you two long paragraphs to explain the difference between a weapon attack and a weapon attack with a weapon illustrates this rather nicely.

Distinguishing "spell/nonspell" or "spell/weapon/unarmed" would've solved the issue without this whole "weapon but not really" song and dance routine.