The Lost ShangriLa - Le ciel bleu profond - Keep Walking, Traveler25

One word derivative of "fate" is "fatality", another "fatalism". Fate implies no choice, and ends fatally,
with a death. Fate is an outcome determined by an outside agency acting upon a person or entity; 
but with destiny the entity is participating in achieving an outcome that is directly related to  itself.
 Participation happens willfully.

There is not much difference, except that 'fate' sometimes (not always!) means 'a bad fate', 'death'.
 'To meet your fate' usually means 'to die'.  Destiny is always neutral.