According to Webster's New World dictionary, "fate" is more about negative things that are sure to happen in the future, while "destiny" is more about positive things that you will meet in the future: "FATE refers to the inevitability of a course of events as supposedly predetermined by a god or other agency beyond human control; DESTINY also refers to an inevitable succession of events as determined supernaturally or by necessity, but often implies a favorable outcome [it was her destiny to become famous ];"

No. Fate is something thing is inevitably going to happen to a person. If someone has an incurable illness, it could be there fate that they are going to die in the next 6 months. Destiny is something that is destined to happen to someone. It is the prince's destiny to inherit the throne once his mother dies. They both mean that something is going to happen to someone and there is no way of preventing this thing from taking place.

Yes, these two words have different meanings. "fate" is something that happens to someone. When someone says something like "On that fateful day", an event has taken place that has changed their life in some way. "destiny" is something that a person can fulfill. If someone says something like "You are destined to pass this test with an A", that means you will most likely get an A on that test. It's more of a future word, explaining something that might happen later on. They have many similarities but they are not exactly the same.