first cousin vs cousin

first cousin and cousin both are nouns.

Word	Noun	Adjective	Verb	Adverb
first cousin	Yes	No	No	No
cousin	Yes	No	No	No

As nouns, first cousin and cousin are synonyms defined as:

Other synonyms of first cousin include cousin-german, full cousin.

first cousin (noun)	cousin (noun)
the child of your aunt or uncle	the child of your aunt or uncle