Peziza domicilina vs cup fungus

Peziza domicilina and cup fungus both are nouns.

Word	Noun	Adjective	Verb	Adverb
Peziza domicilina	Yes	No	No	No
cup fungus	Yes	No	No	No

As nouns, cup fungus is a hypernym of Peziza domicilina; that is, cup fungus is a word with a broader meaning than Peziza domicilina:

Peziza domicilina: a discomycetous fungus of the genus Peziza; the fragile fruiting body is a ghostly white but stains yellow when broken; favors strongly alkaline habitats
cup fungus: any fungus that is a member of the subclass Discomycetes

Other hypernyms of Peziza domicilina include discomycete.

Peziza domicilina (noun)	cup fungus (noun)
a discomycetous fungus of the genus Peziza; the fragile fruiting body is a ghostly white but stains yellow when broken; favors strongly alkaline habitats	any fungus that is a member of the subclass Discomycetes