sprout vs bud

sprout and bud both are nouns.

Word	Noun	Adjective	Verb	Adverb
sprout	Yes	No	Yes	No
bud	Yes	No	Yes	No

As nouns, bud is a hyponym of sprout; that is, bud is a word with a more specific, narrower meaning than sprout:

sprout: any new growth of a plant such as a new branch or a bud
bud: a swelling on a plant stem consisting of overlapping immature leaves or petals

Other hyponyms of sprout include shoot.

sprout (noun)	bud (noun)
a newly grown bud (especially from a germinating seed)	a swelling on a plant stem consisting of overlapping immature leaves or petals
any new growth of a plant such as a new branch or a bud	a partially opened flower

sprout (verb)	bud (verb)
put forth and grow sprouts or shoots	develop buds
produce buds, branches, or germinate	start to grow or develop