Can someone explain the difference between Assignment report and Assigned To report and when you would choose which one?

well... they do different things and show different things on different reports. If you are ever confused, I recommend you create a view with these two fields as 2 columns so you can compare the results for yourself and decide for yourself the best one to choose.

@Kyna Baker - inactive‚ actually wrote a quick tip on this very topic here: https://one.workfront.com/s/question/0D54X00006bluL8SAI/quick-tip-theres-a-difference-between-assignments-and-assigned-to-in-reporting -- this covers how your basic view or filter would function in any task or issue report.

To summarize: create a view with any fields that you're not sure about and the report columns will always make it clear what that field is storing. This becomes extremely important the moment you move into a report that uses this same field name to mean something completely different, like an Assignment report which uses Assigned To in a different way than a Task report does.