identity vs indistinguishability

identity and indistinguishability both are nouns.

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

As nouns, identity and indistinguishability are synonyms defined as:

Other synonyms of identity include identicalness.

identity (noun)	indistinguishability (noun)
the distinct personality of an individual regarded as a persisting entity	exact sameness
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