tomato plant vs herb

tomato plant and herb both are nouns.

Word	Noun	Adjective	Verb	Adverb
tomato plant	Yes	No	No	No
herb	Yes	No	No	No

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

tomato plant: native to South America; widely cultivated in many varieties
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 tomato plant include herbaceous plant.

tomato plant (noun)	herb (noun)
native to South America; widely cultivated in many varieties	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