star anise vs star aniseed

star anise and star aniseed both are nouns.

Word	Noun	Adjective	Verb	Adverb
star anise	Yes	No	No	No
star aniseed	Yes	No	No	No

As nouns, star anise and star aniseed are synonyms defined as:

star anise and star aniseed: anise-scented star-shaped fruit or seed used in Asian cooking and medicine

Other synonyms of star anise include Chinese anise.

star anise (noun)	star aniseed (noun)
anise-scented star-shaped fruit or seed used in Asian cooking and medicine	anise-scented star-shaped fruit or seed used in Asian cooking and medicine
small tree of China and Vietnam bearing anise-scented star-shaped fruit used in food and medicinally as a carminative
small shrubby tree of Japan and Taiwan; flowers are not fragrant