purple anise vs anise tree

purple anise and anise tree both are nouns.

Word	Noun	Adjective	Verb	Adverb
purple anise	Yes	No	No	No
anise tree	Yes	No	No	No

As nouns, anise tree is a hypernym of purple anise; that is, anise tree is a word with a broader meaning than purple anise:

purple anise: small shrubby tree with purple flowers; found in wet soils of southeastern United States
anise tree: any of several evergreen shrubs and small trees of the genus Illicium

purple anise (noun)	anise tree (noun)
small shrubby tree with purple flowers; found in wet soils of southeastern United States	any of several evergreen shrubs and small trees of the genus Illicium