Fate vs. Destiny

A couple days ago I was asked by a Swiss woman (who is fluent in English) to explain to her the difference between "fate" and "destiny". I told her that was a tough one and that I'd need to think about it a bit. Any suggestions? She used "destiny" in the context of "Roger Federer (local Swiss tennis player who just won the US Open) followed his destiny". The Swiss, and particularly those who live in Basel as his "neighbor", are very proud of Roger Federer.