tobacco plant vs herb

tobacco plant and herb both are nouns.

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

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

tobacco plant: aromatic annual or perennial herbs and shrubs
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 tobacco plant include herbaceous plant.

tobacco plant (noun)	herb (noun)
aromatic annual or perennial herbs and shrubs	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