There is a clear purpose for Evaluation Rights vs. Assigning Forms. Assigning forms should not be confused with Evaluator rights.
Evaluator Rights allows multiple evaluators to see the process for one individual user.
Assigning forms tells the system which of the possible multiple administrators with Evaluator Rights is ultimately responsible for completing/finalizing a form/component. Assigning forms is more of an "accountability" issue than a "rights" issue.
The Admin View on the left navigation bar shows forms assigned to an administrator.
The Process View shows all users an evaluator have rights to see (Evaluation Rights).
The Detail View could show either depending upon how the columns are filtered. The default Detail View is everything the designated administrator has rights (Evaluations Rights) to view. You could filter the forms assigned to you via "Admin Column" and create a view just for those forms you are responsible for (Assign Form).
If the evaluator is in two buildings, the evaluator could filter Detail View by building to see one vs. the other.
NOTE: Technically, forms do not need to be assigned. If district personnel do not care about which administrator is assigned to which users' forms, they don't need to assign forms. However, not assigning forms will result in an incomplete view in the Admin View and the Super Admin View.