first cousin vs full cousin

first cousin and full cousin both are nouns.

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

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

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

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