Nihilism: Do whatever you want because nothing matters.
Nihilist believe there is no "meaning" in life because there is no objective truth in the world.
Existentialism: Do whatever you want because it matters to you.
Existentialists know that there is no objective truth in world, so instead of saying there is no purpose, they make their own purposes to do whatever they want.
Basically, existentialism are concerned about finding a meaning while Nhilism denies that there is no meaning.
I think your final sentence should read ..."while Nhilism (sic) holds that there is no meaning." Or... "while Nhilism (sic) denies that there is meaning."
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