In general terms, yes, I believe you understand the differences, but the word "during" is also important.
I think the contrast is more between "during the last/past week" and "last week".
With the first you can use the present perfect tense. The use of present perfect will force a reading of "during the past seven days ending today".
The use of the words "during the last" or "during the past" is important to clarify that the time period extends into present time. If the time period extends up to the present, the present perfect can be used; otherwise, not.
During the past week, we have answered many questions.
During the last week, they have seen two elephants and three tigers.
But:
Last week we have answered many questions. (Wrong. Last week has ended. Otherwise we would have said "this week".)
Last week we answered many questions. (Correct.)
During the last week of their African safari in 1998, they have seen two elephants and three tigers. (Wrong. The seeing does not extend into present time.)
During the last week of ..., they
saw two elephants ... (Correct.)
I'm not sure if that answers all your questions, but you can always post again if necessary!