identity element vs identity operator

identity element and identity operator both are nouns.

Word	Noun	Adjective	Verb	Adverb
identity element	Yes	No	No	No
identity operator	Yes	No	No	No

As nouns, identity element and identity operator are synonyms defined as:

identity element and identity operator: an operator that leaves unchanged the element on which it operates

Other synonyms of identity element include identity.

identity element (noun)	identity operator (noun)
an operator that leaves unchanged the element on which it operates	an operator that leaves unchanged the element on which it operates