Adiantaceae vs fern family

Adiantaceae and fern family both are nouns.

Word	Noun	Adjective	Verb	Adverb
Adiantaceae	Yes	No	No	No
fern family	Yes	No	No	No

As nouns, fern family is a hypernym of Adiantaceae; that is, fern family is a word with a broader meaning than Adiantaceae:

Adiantaceae: used in some classification systems for some genera of the family Polypodiaceae (or Pteridaceae)
fern family: families of ferns and fern allies

Adiantaceae (noun)	fern family (noun)
used in some classification systems for some genera of the family Polypodiaceae (or Pteridaceae)	families of ferns and fern allies