lily of the Incas vs Peruvian lily

lily of the Incas and Peruvian lily both are nouns.

Word	Noun	Adjective	Verb	Adverb
lily of the Incas	Yes	No	No	No
Peruvian lily	Yes	No	No	No

As nouns, lily of the Incas and Peruvian lily are synonyms defined as:

lily of the Incas and Peruvian lily: an Andean herb having umbels of showy pinkish-purple lily-like flowers

Other synonyms of lily of the Incas include Alstroemeria pelegrina.

lily of the Incas (noun)	Peruvian lily (noun)
an Andean herb having umbels of showy pinkish-purple lily-like flowers	an Andean herb having umbels of showy pinkish-purple lily-like flowers