Clavariaceae vs fungus family

Clavariaceae and fungus family both are nouns.

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

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

Clavariaceae (noun)	fungus family (noun)
fleshy fungi: coral fungi	includes lichen families