Here's what I got:
Both are translated as a salutation -at times with a reference to God-, and are quite interchangeable, but they have different origins.
- Ave comes from the imperative form of aveo, which means to be/fare well.
- Salve comes from the imperative form of salveo, to be well/in good health. Note that this health can be physical or spiritual -salvation-, (hence God save you.)
So both are basically be well, but an emphasis -if any- might be implied in performance (ave) or health (salve).
I think the etymology means the distinction should have been valid, at least at the beginning. In contrast, ave has also been translated as God save you, e.g. at least in translations of the Hail Mary (or Lc 1, 28) to Spanish, Aragonese, Catalan and Sardinian (the Greek version uses χαῖρε as salutation, which means rejoice).