schopenhauer and nietzsche were both considered 'vitalists', but nietzsche wanted to extend the notion of biological power to physis, to mechanical power; the will to life is not explanatory... there must also be a will in the very mechanism of all things before they even become biological. although schopenhauer also called the phenomenal world a 'representation' of the noumenal world of 'will' (which he inherited from kant), he did not claim that the will which represented the world was about 'power'. this was one of nietzsche's breaks with schopenhauer.
nietzsche abhored schopenhauer's pessimism, so he set out to put a different spin on the concept of the transcendental 'will'; suffering and striving are consequences of weakness of will, not of will itself, as schopenhauer had it. life is NOT inherently bad, and the judgement 'bad' reflects only a physiology and/or psychology of the one who makes the judgement. a judgement is a symptom only. schopenhauer was sick, but not a pure pessimist because he played the flute. nietzsche gave him that much credit.
then later nietzsche realizes he's misled everyone by calling it a 'will' to power in a fundamental sense. he explicitly admits that there is no 'will' countless times throughout his work.
why then the doctrine? because he had to explain the direction and process of becoming and change, indicatively. why there is change and becoming. for his purposes he anthropomorphizes becoming and change so that we can think of it as a vitalistic process, a metaphysical process; why do things evolve and change? because they have an inner will, are directed by an inner will, to do so. and what are they willing? not just life, but power.
that was nietzsche's original thesis.
but there is no 'Will' with a capital W. when we talk about 'will' we mean to say that someone or something is acting voluntarily and with purpose. and it makes no difference whether you are a hard-determinist, compatibalist, or indeterminist, for the word to be meaningful in language.
joe is taking a metaphysics-free walk to the store because he's willed it, because he wants to go to the fucking store and buy a pepsi, a snickers bar, and a lottery ticket (i don't know why because joe has a better chance of getting struck by lightening than winning the lottery). joe has the will and he knows the way. nuff said.
wanna know what the WTP is? not a rudimentary force, not the most fundamental fact, .... but this.
there you have it. these arguments at ILP that go back and forth endlessly, splitting hairs and quibbling over the definition of the WTP, are driving me bonkers.