In which cases is present perfect equal to simple past?

In which cases present perfect is equal (exactly or in common usage) to past tense? For example, these two questions have pretty much no difference in common usage (as far as I'm aware):

"Have I got it right?"

and

"Did I get it right?"

When grammar book teaches the rules of the English language it often explains the tenses by listing the kinds of actions or situations in which the tense is used. For example, the present perfect tense is used for actions completed in the very recent past, etc. This is the kind of answer I expect. But if you have another way to answer, please do it your way.

Solution 1:

Both refer to the past. It is question of the immediacy of the events.

Say we met yesterday and you asked me a question. We parted ways for you to consider my answer. When we meet today I might ask: "Did I get it right?" as my answer was not given in the immediate past.

If we meet today and you ask me a question which I answer and I immediately want to know if my answer is correct, I might ask: "Have I got it right?"