genus Mammuthus vs mammal genus

genus Mammuthus and mammal genus both are nouns.

Word	Noun	Adjective	Verb	Adverb
genus Mammuthus	Yes	No	No	No
mammal genus	Yes	No	No	No

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

genus Mammuthus (noun)	mammal genus (noun)
extinct genus: mammoths	a genus of mammals