genus Cuculus vs bird genus

genus Cuculus and bird genus both are nouns.

Word	Noun	Adjective	Verb	Adverb
genus Cuculus	Yes	No	No	No
bird genus	Yes	No	No	No

As nouns, bird genus is a hypernym of genus Cuculus; that is, bird genus is a word with a broader meaning than genus Cuculus:

genus Cuculus (noun)	bird genus (noun)
type genus of the Cuculidae	a genus of birds