Can I move something from the assignment category over to a module? And Vice versa?
Welcome to the Canvas Community!
You can't move it from an assignment category to a Module but you can add it to a Module:
How do I add assignment types, pages, and files as module items?
The Assignments tool is where the assignment and the assignment group is created and will always live. The Modules tool is more of an organizational tool than a content creation tool although you can create placeholders for assignments and such.
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