You can have assignments to do during a class so not all assignments are homework assignments. "homework" is general, uncountable "a homework assignment" is a specific task to do as part of your homework.

Anything assigned to you is an assignment. The homework is assigned to you. Homework is collective. You have homework or not, you don't have homeworks. I have 3 homework assignments. I have lots of homework, I have 3 assignments. Yes it does not really answer your question, it just explains how to use it.:)

Hi! I had never thought about it before, but you’re right—it is redundant to say “homework assignment.” If you said “homework” by itself you’d be perfectly understood, but if you just said “assignment” you may need to clarify by saying that you’re doing it for school or a class, not for work. Hope that helps!