African lily vs agapanthus

African lily and agapanthus both are nouns.

Word	Noun	Adjective	Verb	Adverb
African lily	Yes	No	No	No
agapanthus	Yes	No	No	No

As nouns, agapanthus is a hypernym of African lily; that is, agapanthus is a word with a broader meaning than African lily:

African lily: African plant with bright green evergreen leaves and umbels of many usually deep violet-blue flowers
agapanthus: any of various plants of the genus Agapanthus having umbels of showy blue to purple flowers

Other hypernyms of African lily include lily of the Nile.

African lily (noun)	agapanthus (noun)
African plant with bright green evergreen leaves and umbels of many usually deep violet-blue flowers	any of various plants of the genus Agapanthus having umbels of showy blue to purple flowers