Are Assignment Category and Task list group the same thing or similar?

No, the Assignment Category and the Task list Group are different. The Assignment Category is a way of furthering categorising the type of work you’re doing.  For example, the Category could be Daily, Weekly or Monthly and the Assignment Type is an Audit.

The Task List Group is one of the tasks that you complete as a part of the Audit. For example, this could be a Risk Assessment.