asparagus fern vs herb

asparagus fern and herb both are nouns.

Word	Noun	Adjective	Verb	Adverb
asparagus fern	Yes	No	No	No
herb	Yes	No	No	No

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

asparagus fern: a fernlike plant native to South Africa
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 fern include herbaceous plant.

asparagus fern (noun)	herb (noun)
a fernlike plant native to South Africa	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