indistinguishability vs identity

indistinguishability and identity both are nouns.

Word	Noun	Adjective	Verb	Adverb
indistinguishability	Yes	No	No	No
identity	Yes	No	No	No

As nouns, indistinguishability and identity are synonyms defined as:

Other synonyms of indistinguishability include identicalness.

indistinguishability (noun)	identity (noun)
exact sameness	the distinct personality of an individual regarded as a persisting entity
	exact sameness
	the individual characteristics by which a thing or person is recognized or known
	an operator that leaves unchanged the element on which it operates