In daily language destiny and fate are synonymous, but with regards to 20th century philosophy the words gained inherently different meanings.
For Arthur Schopenhauer destiny was just a manifestation of the Will to Live. Will to Live is for him the main aspect of the living. The animal cannot be aware of the Will, but men can at least see life through its perspective, though it is the primary and basic desire. But this fact is a pure irrationality and then, for Schopenhauer, human desire is equally futile, illogical, directionless, and, by extension, so is all human action. Therefore, the Will to Live can be at the same time living fate and choice of overrunning the fate same, by means of the Art, of the Morality and of the Ascesis.
For Nietzsche destiny keeps the form of Amor fati (Love of Fate) through the important element of Nietzsche's philosophy, the "will to power" (der Wille zur Macht), the basis of human behavior, influenced by the Will to Live of Schopenhauer. But this concept may have even other senses, although he, in various places, saw the will to power as a strong element for adaptation or survival in a better way. In its later forms Nietzsche's concept of the will to power applies to all living things, suggesting that adaptation and the struggle to survive is a secondary drive in the evolution of animals, less important than the desire to expand one’s power. Nietzsche eventually took this concept further still, and transformed the idea of matter as centers of force into matter as centers of will to power as mankind’s destiny to face with amor fati.
The expression Amor fati is used repeatedly by Nietzsche as acceptation-choice of the fate, but in such way it becomes even another thing, precisely a “choice” destiny.
Ed tells me that the above strikes him as "gibberish." Well, if not pure gibberish, then very, very bad. First of all, the writing is awkward and inept and in places incoherent.
In the first sentence the author mentions 20th century philosophy and then immediately goes on to speak of Schopenhauer and Nietzsche, both 19th century thinkers. Could the author be so clueless as not to know when these gentlemen lived and wrote?
"Will to Live is the main aspect of the living." Sentences like his are part of why I rejoice in no longer being a professor. First of all, Will cannot be described as an aspect of anything: 'aspect' suggests a view, an appearance, a representation (Vorstellung), a phenomenon. Schopenhauer's Will, however, plays in his system the role that the thing-in-itself (Ding an sich) plays in Kant's. Will is noumenal, not phenomenal, and so cannot be coherently described as an aspect. One ought to have gathered this just from the title of Schopenhauer's magnum opus, Die Welt als Wille und Vorstellung. Second, Will is what everything is at bottom, not just living things.
I won't continue through the passage. It is bad throughout. What I hated about teaching was having to wade through garbage like this. How does one explain to an incompetent writer what competent writing is? It is like trying to explain to a nerd why his pocket protector is a sartorial outrage or why pulling your pants up too high is 'uncool' or why socks with sandals don't make it. Or how do you explain to a socially lame person why she is socially lame? What do you do? Give her rules to follow? But such rules come too late.
I do not take as harsh a view of Wikipedia as Ed does. There is much of value in its pages, and plenty of the material is arcana that cannot be found elsewhere. But one cannot really trust anything one finds there since there is no way of knowing who wrote what and what his credentials are.
Let Caveat lector! be your watch-phrase, then, when you make use of this online resource.
Addendum: Mark Anderson recommends The 'Undue Weight' of Truth on Wikipedia.