lily family vs genus Allium

lily family and genus Allium both are nouns.

Word	Noun	Adjective	Verb	Adverb
lily family	Yes	No	No	No
genus Allium	Yes	No	No	No

lily family (noun)	genus Allium (noun)
includes species sometimes divided among the following families: Alliaceae, Aloeaceae, Alstroemeriaceae, Aphyllanthaceae, Asparagaceae, Asphodelaceae, Colchicaceae, Convallariaceae, Hemerocallidaceae, Hostaceae, Hyacinthaceae, Melanthiaceae, Ruscaceae, Smilacaceae, Tecophilaeacea, Xanthorrhoeaceae	large genus of perennial and biennial pungent bulbous plants: garlic, leek, onion, chive; sometimes placed in family Alliaceae as the type genus