The disparities are nuanced. If I had to say, fate would be something that is certain to happen in the future due to a grand scheme (i.e. forces of nature), whereas destiny is something that must be realized and achieved by the individual, even if the individual has been granted the potential to do so.
For example, moving away from your girlfriend to go to college then reuniting with her 6 years later in another state because you both got a job at the same company is fate. Assuming power of the company you work for after the owner (who is your mentor) dies would be destiny.