"She had assigned" vs "She has assigned"

Both are grammatical and both make sense but the verb 'assigned' is in a different tense in each case so the time frame is different.

In the first case 'assigned' is in the present perfect tense because the auxiliary verb is 'has' so the speaker is talking about an assignment which is still in force and the sentence is actually about the assignment. For example a longer version of the sentence might be:

"She has assigned topics for everyone and given me Macbeth."

In the second case 'assigned' is in the past perfect tense because the auxiliary verb is 'had'. This means that the action of assignment took place before something else happened. In this case (A) there either has to be more to the sentence to tell us what else happened or (B) there has to be some context in the conversation. Examples are:

(A) "She had assigned topics for everyone and given me Macbeth but I said 'I haven't read or seen Macbeth, can't I have The Tempest?"

or

(B) Someone else might say "What happened to cause the argument with your teacher?" and you might reply "She had assigned topics for everyone and given me Macbeth but I've never seen nor read Macbeth so I asked for The Tempest and she said I had to work on the topic she'd given me"

In both of case A and case B the assignment topics was completed before some other action took place.