lily family vs family Alliaceae

lily family and family Alliaceae both are nouns.

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

lily family (noun)	family Alliaceae (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	one of many families or subfamilies into which some classification systems subdivide the Liliaceae but not widely accepted; includes especially genus Allium