equivalence vs equality

equivalence and equality both are nouns.

Word	Noun	Adjective	Verb	Adverb
equivalence	Yes	No	No	No
equality	Yes	No	No	No

As nouns, equality is a hypernym of equivalence; that is, equality is a word with a broader meaning than equivalence:

equivalence: essential equality and interchangeability
equality: the quality of being the same in quantity or measure or value or status

As nouns, equivalence and equality are synonyms defined as:

equivalence and equality: a state of being essentially equal or equivalent; equally balanced

Other synonyms of equivalence include equation, par.

equivalence (noun)	equality (noun)
qualities that are comparable	the quality of being the same in quantity or measure or value or status
essential equality and interchangeability	a state of being essentially equal or equivalent; equally balanced
a state of being essentially equal or equivalent; equally balanced