Pezizaceae vs fungus family

Pezizaceae and fungus family both are nouns.

Word	Noun	Adjective	Verb	Adverb
Pezizaceae	Yes	No	No	No
fungus family	Yes	No	No	No

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

Pezizaceae (noun)	fungus family (noun)
large family comprising many typical cup fungi	includes lichen families