parity vs equivalence

parity and equivalence both are nouns.

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

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

parity (noun)	equivalence (noun)
functional equality	qualities that are comparable
(physics) parity is conserved in a universe in which the laws of physics are the same in a right-handed system of coordinates as in a left-handed system	essential equality and interchangeability
(computer science) a bit that is used in an error detection procedure in which a 0 or 1 is added to each group of bits so that it will have either an odd number of 1's or an even number of 1's; e.g., if the parity is odd then any group of bits that arrives with an even number of 1's must contain an error	a state of being essentially equal or equivalent; equally balanced
(mathematics) a relation between a pair of integers: if both integers are odd or both are even they have the same parity; if one is odd and the other is even they have different parity
(obstetrics) the number of liveborn children a woman has delivered