bay leaf vs herb

bay leaf and herb both are nouns.

Word	Noun	Adjective	Verb	Adverb
bay leaf	Yes	No	No	No
herb	Yes	No	No	No

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

bay leaf (noun)	herb (noun)
dried leaf of the bay laurel	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