gesture vs wave

gesture and wave both are nouns.

Word	Noun	Adjective	Verb	Adverb
gesture	Yes	No	Yes	No
wave	Yes	No	Yes	No

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

gesture: the use of movements (especially of the hands) to communicate familiar or prearranged signals
wave: the act of signaling by a movement of the hand

As verbs, wave is a hyponym of gesture; that is, wave is a word with a more specific, narrower meaning than gesture:

gesture (noun)	wave (noun)
motion of hands or body to emphasize or help to express a thought or feeling	a movement like that of a sudden occurrence or increase in a specified phenomenon
something done as an indication of intention	a hairdo that creates undulations in the hair
the use of movements (especially of the hands) to communicate familiar or prearranged signals	the act of signaling by a movement of the hand
	(physics) a movement up and down or back and forth
	one of a series of ridges that moves across the surface of a liquid (especially across a large body of water)
	something that rises rapidly
	a persistent and widespread unusual weather condition (especially of unusual temperatures)
	an undulating curve

gesture (verb)	wave (verb)
show, express or direct through movement	set waves in
	signal with the hands or nod
	move or swing back and forth
	twist or roll into coils or ringlets
	move in a wavy pattern or with a rising and falling motion