lily family vs liliid monocot family

As nouns, liliid monocot family is a hypernym of lily family; that is, liliid monocot family is a word with a broader meaning than lily family:

• lily family: includes species sometimes divided among the following families: Alliaceae, Aloeaceae, Alstroemeriaceae, Aphyllanthaceae, Asparagaceae, Asphodelaceae, Colchicaceae, Convallariaceae, Hemerocallidaceae, Hostaceae, Hyacinthaceae, Melanthiaceae, Ruscaceae, Smilacaceae, Tecophilaeacea, Xanthorrhoeaceae
• liliid monocot family: family of monocotyledonous plants of the subclass Liliidae; mostly herbs usually with petaloid sepals and petals and compound pistils