They are supposed to be synonyms. "destiny" reached English from Latin "destinata" through French "destiné" (= what has been established), whereas "fate" comes directly from Latin "fatum" (= what has been said [by the gods]). Both refer to what is bound to occur because it has so been determined by supernatural forces (God, etc.). However, in current usage, "destiny" does not seem to be as strong and irrevocable as "fate" is. In English, as in other languages, it is not uncommon for politicians to more or less solemnly and rhetorically proclaim things like "From now on, we (the people, this country, etc.) is/are in/take(s) control of our/its destiny....". On the contrary, the expression "?...control / take control of ... Fate" is unthinkable. What we understand by "Fate" is beyond our control; what we understand by "destiny" is not, or not to the same extent. So our use of the respective terms seems to indicate, anyway.