Fate is what happens to you and out of your control, while destiny is what results from your actions.
Fate is what one is locked into; destiny is what one develops by elective choice.
Fate is something that is unavoidable, an inevitable course of events.

According to Hindu thought, man is not ruled by fate but shapes his own destiny by his actions, which have their concomitant reactions.


Destiny vs. fate
Although the words are used interchangeably, fate and destiny are distinct things. “Fate” is normally used in the past tense after the course of event has happened, but Destiny happens when one takes a particular path, if he changes the path, he can change his destiny. Fate is an outcome determined by an outside agency acting upon a person or entity; Example... an ill fated plane travel, or train travel... Destiny the entity is participating in achieving an outcome that is directly related to it... Destiny may be seen as fixed sequence events that are inevitable and unchangeable, or that individuals choose their own destiny by choosing different paths throughout their life. Destiny can be changed or controlled if a particular path is changed... once a particular path is taken one is distained to reach its outcome.

Destiny is a matter of Choice but Fate is finality.

Fate, Free Will and Vedic Astrology

In our lives we are often faced with choices presented to us by our environmental circumstances. We have the freedom to chose "a" or "b," but once that decision is made we must accept the reaction to our choice. Thus, life is interplay of both fate and free will.
Let's consider an example of how this works. Suppose someone is born into a poor family because of his bad karma from a previous lifetime and so is raised in a ghetto beset with crime and poverty. Let us say, hypothetically, that he has two choices. He can blame society for the evils he faces and thus try to victimize society by taking to a life of crime to acquire wealth; or he can take responsibility for his situation and try to better himself by education and honest endeavor. Suppose he chooses the first option of crime and robs several establishments. Eventually he will get caught (if not killed first) and sent to jail, a natural reaction for his criminal behavior. But even while in jail he still has options, though more limited than those of a free man. He can choose to be a hardened criminal or to be a model prisoner and reform himself. Each choice will have a reaction. Thus we can see that life is an intricate interplay of fate/destiny (karma) and free will.

A horoscope in your hands is a map of destiny, and predictions can be changed if a different path is taken
The birth-map, or horoscope, is a symbolic representation of the Earth, planets, and stars at the time of one's birth. It is a divine language, a mystic cryptogram by which God has communicated what a person's destiny will be; knowing which a wise person will exercise his free will (Thought Theory) to optimize the result.
Now let us discuss about Free will or Thought theory

Thought Theory believes in making one's own destiny through his words, deeds and thoughts. He believes in totally accepting responsibility for his failures and misfortunes. At every point of one's life God gives you choices, and once you choose a choice you are distained to reach its result

Let us discuss this point further:

Neither karma nor astrology point to a rigid and immutable fate. Stars don’t rule over our destiny. Stars merely record a destiny that has already been formed. They are only indicators and they often indicate several fate possibilities.

Astrologers themselves say that there are two forces daiva and purusakara, i.e. fate and individual energy and the individual energy can modify and even frustrate fate.

The People who lost their lives were in the train accident were in wrong place at wrong time and Fate snatched them away, it is like one is caught in mob attack in market unknowingly, or a terrorist attack in a crowded place.

The list of wars and human-made disasters by death toll including Genocides and alleged genocides, extermination camps, Famine, Human sacrifices and man made mass mortalities.

Each one of the above subject is very big.