When I was a Moral Nihilist, it was because I would look from a sort of "universal" point of view at Moral Relativism. "Outside all morals, there are no morals." I did a similar thing with "from the Universe's perspective, my life is an incredibly small blip on the radar", to arrive at regular Nihilism as well.
The thing I failed to realise, and what later made me move away from Nihilism, was that I had simply made up this point of view and hadn't really left my own point of view at all. This revealed to me the internal inconsistency of thinking this "universal" point of view, even if it wasn't a figment of my own perspective's imagination, was anymore priveledged than the other points of view. The very premises of relativity deny a priveledged frame of reference. So if morality exists in one frame, it exists, and if value exists in one frame, it exists. The fact that they may not exist in other frames does not take away from that. So Nihilism could not successfully deny those thing's existence as I once thought it could.
Both "Outside all morals, there are no morals" and "compared to the universe, my life is an incredibly small blip on the radar" remain true, but any significance they once had is lost.
So Moral Nihilism, meaning either that "all moral facts are false" or that "moral facts don't exist", directly contradicts Moral Relativity, meaning that "moral facts are relative/subjective".