Phallaceae vs fungus family

Phallaceae and fungus family both are nouns.

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

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

Phallaceae: a family of fungi belonging to the order Phallales and comprising the true stinkhorns
fungus family: includes lichen families

Phallaceae (noun)	fungus family (noun)
a family of fungi belonging to the order Phallales and comprising the true stinkhorns	includes lichen families