Difference between "fate" and "destiny"
What is the difference between "fate" and "destiny"? Can I use them as synonyms? I think "fate" is the generic term for everything that can happen to an individual or a group of individuals.
The “Fault In Our Stars” (John Green, 2012) refers to the life history of young people suffering from terminal cancer.
I’ve read that Green’s title choice was inspired by Shakespeare: "The fault, dear Brutus, is not in our stars, / But in ourselves, that we are underlings."
"Destiny" has a more general meaning and refers to everything happening without any human control. Would you accept this distinction? If not, can you help me with examples, please? Thank you.

Question

Difference between "fate" and "destiny"
What is the difference between "fate" and "destiny"? Can I use them as synonyms? I think "fate" is the generic term for everything that can happen to an individual or a group of individuals. 
The “Fault In Our Stars” (John Green, 2012) refers to the life history of young people suffering from terminal cancer. 
I’ve read that Green’s title choice was inspired by Shakespeare: "The fault, dear Brutus, is not in our stars, / But in ourselves, that we are underlings." 
"Destiny" has a more general meaning and refers to everything happening without any human control. Would you accept this distinction? If not, can you help me with examples, please? Thank you.

Answer

They mean more or less the same thing, but the connotations are opposite. I would say that “fate” has negative connotations (think of those ancient Greek goddesses spinning yarn, measuring it, and cutting it off), while “destiny” tends to have good ones. Also, I would use “fate” to refer to both the past and future, but “destiny” usually refers to the events which have not yet occurred.

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That seems like a reasonable distinction, but I agree with Vanessa that they are generally used as synonyms.

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"You can influence your destiny" - but not your fate?! Interesting thought. The differences seem to be very subtle if I consider the power of will, time and coincidence which determine my personal development. Terminal-ill people may have the will to change their individual fate, but "the stars" have predetermined another way. Although people* try to improve the quality of life and reconcile with the inevitable, their fate is sealed. Thank you, Fred.

*edited for clarity in the choice of words...

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I think there is a big difference.. I think of fate as an already predetermined and sealed. It is divinely connected and sadly no one can do anything about it. If used it is to the negative. 
But for destiny, anybody creates their destiny. What you want to become. It can be good or bad. You can influence your destiny

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Thank you, Vanessa.