Is Moral Nihilism a Morality?

[SenseMaker007]

Is there a difference between normative and logical correctness in moral realism?

Yes, because the latter only deals with metaethics. Saying "moral realism is false" doesn't mean "moral realism is morally wrong" and saying "moral realism is true" doesn't mean "moral realism is morally right." Those would be additional normative statements added on top of the metaethics. You'd at the very least have to also believe that the truth is morally good, and falsehood is morally bad, in addition to that, first.

Moral realism can be true, and you can, therefore, be correct to believe in it (logically correct, not morally correct), without you making any normative statements. And moral realism can be false, and you can, therefore, to be correct to not believe in it (logically correct, not morally correct), but you can still make normative statements. A nihilist can make a normative statement and say "I ought to do X", despite the fact that it contradicts their own position and a moral realist can refrain from making normative statements, and never say anything like "I ought to do X", or anything similar, regardless of the fact that they're a moral realist. Whoever is right and whoever is wrong doesn't change who is making normative statements and who isn't.

What I actually said was that saying that moral nihilism is logically incorrect and incoherent isn't making a normative statement or saying that nihilism is morally wrong.