cup fungus vs ascomycete

cup fungus and ascomycete both are nouns.

Word	Noun	Adjective	Verb	Adverb
cup fungus	Yes	No	No	No
ascomycete	Yes	No	No	No

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

cup fungus: any fungus that is a member of the subclass Discomycetes
ascomycete: any fungus of the class Ascomycetes (or subdivision Ascomycota) in which the spores are formed inside an ascus

Other hypernyms of cup fungus include ascomycetous fungus.

cup fungus (noun)	ascomycete (noun)
any fungus that is a member of the subclass Discomycetes	any fungus of the class Ascomycetes (or subdivision Ascomycota) in which the spores are formed inside an ascus