Fate is more deterministic, I think the fatalists would choose this word more times than not.
Have a more negative ring too. For example: If you´re fated to failure (Se você é fadado ao fracasso, "doomed" to failure).
See the synonyms (the majority of them are 'negative' in meaning. Albeit, not necessarily (not always) =>
Synonyms: circumstances (n), destiny (n), fortune (n), lot (n), luck (n), portion (n),
designate (v), destine (v), doom (v).
More some =>
Predetermination Noun: predestination, preordination, premeditation, predeliberation, predetermination;
foregone conclusion, fait accompli; parti pris; resolve, propendency; intention; project;
fate, foredoom, necessity.
Destiny has more of a "prospect or futurity" and an "existence" quality in it.
In practice they can be interchangeable, the context is what will restrict the meaning.
So, my advice is read and look up in a dictionary for examples. Practice makes perfect.
1. An event (or course of events) that will inevitably happen in the future.
2. The ultimate agency that predetermines the course of events (often personified as a woman); "we are helpless in the face of Destiny".
3. Your overall circumstances or condition in life (including everything that happens to you): "whatever my fortune may be"; "deserved a better fate"; "has a happy lot"; "the luck of the Irish"; "a victim of circumstances"; "success that was her portion".
1. Decree or designate beforehand; "She was destined to become a great pianist".
Definition: the same above.
Synonyms within Context: Destiny
Context Synonyms within Context (source: adapted from Roget's Thesaurus).
Destiny Noun: destiny; (necessity); future existence, post existence; hereafter; future state, next world, world to come, after life; futurity; everlasting life, everlasting death; life beyond the grave, world beyond the grave; prospect; (expectation).
Expectation Contemplation, prospection, lookout; prospect, perspective, horizon, vista; destiny.
Futurity Approach of time advent, time drawing on, womb of time; destiny; eventuality.
Necessity Destiny, destination; fatality, fate, kismet, doom, foredoom, election, predestination; preordination, foreordination; lot fortune; fatalism; inevitableness; Adjective: spell.
Obstinacy Die hard, fight against destiny, not yield an inch, stand out.