supremacy vs dominance

supremacy and dominance both are nouns.

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

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

supremacy: power to dominate or defeat
dominance: the state that exists when one person or group has power over another

Other hypernyms of supremacy include ascendance, ascendancy, ascendence, ascendency, control.

supremacy (noun)	dominance (noun)
power to dominate or defeat	the power or right to give orders or make decisions
	superior development of one side of the body
	the organic phenomenon in which one of a pair of alleles present in a genotype is expressed in the phenotype and the other allele of the pair is not
	the state that exists when one person or group has power over another