superiority vs supremacy

superiority and supremacy both are nouns.

Word	Noun	Adjective	Verb	Adverb
superiority	Yes	No	No	No
supremacy	Yes	No	No	No

As nouns, supremacy is a hypernym of superiority; that is, supremacy is a word with a broader meaning than superiority:

superiority: the state of excelling or surpassing or going beyond usual limits
supremacy: power to dominate or defeat

Other hypernyms of superiority include domination, mastery.

superiority (noun)	supremacy (noun)
the quality of being superior	power to dominate or defeat
the quality of being at a competitive advantage
displaying a sense of being better than others
the state of excelling or surpassing or going beyond usual limits