Asparagus officinales vs herb

Asparagus officinales and herb both are nouns.

Word	Noun	Adjective	Verb	Adverb
Asparagus officinales	Yes	No	No	No
herb	Yes	No	No	No

As nouns, herb is a hypernym of Asparagus officinales; that is, herb is a word with a broader meaning than Asparagus officinales:

Asparagus officinales: plant whose succulent young shoots are cooked and eaten as a vegetable
herb: a plant lacking a permanent woody stem; many are flowering garden plants or potherbs; some having medicinal properties; some are pests

Other hypernyms of Asparagus officinales include herbaceous plant.

Asparagus officinales (noun)	herb (noun)
plant whose succulent young shoots are cooked and eaten as a vegetable	aromatic potherb used in cookery for its savory qualities
	a plant lacking a permanent woody stem; many are flowering garden plants or potherbs; some having medicinal properties; some are pests