first cousin vs cousin-german

first cousin and cousin-german both are nouns.

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

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

Other synonyms of first cousin include cousin, full cousin.

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