Berberis vulgaris vs barberry

Berberis vulgaris and barberry both are nouns.

Word	Noun	Adjective	Verb	Adverb
Berberis vulgaris	Yes	No	No	No
barberry	Yes	No	No	No

As nouns, barberry is a hypernym of Berberis vulgaris; that is, barberry is a word with a broader meaning than Berberis vulgaris:

Berberis vulgaris: upright deciduous European shrub widely naturalized in United States having clusters of juicy berries
barberry: any of numerous plants of the genus Berberis having prickly stems and yellow flowers followed by small red berries

Berberis vulgaris (noun)	barberry (noun)
upright deciduous European shrub widely naturalized in United States having clusters of juicy berries	any of numerous plants of the genus Berberis having prickly stems and yellow flowers followed by small red berries