First, I think you mean "letter," not "later." Second, we use the present perfect for a time starting in the past and continuing until now. So if I mailed the letter four days ago, I might ask, "Have you received my letter?" If I sent it two months ago, I would probably ask, "Did you receive my letter?" This is because I assume it was delivered months ago, and I am just asking the other person to confirm this.

No difference. They're both wrong! If you mean a "letter", then there is no difference in practical meaning here. In both cases he is asking: ""Do you have the letter?"