lily family vs Allium

lily family and Allium both are nouns.

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

lily family (noun)	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