waving vs flourish

waving and flourish both are nouns.

Word	Noun	Adjective	Verb	Adverb
waving	Yes	No	No	No
flourish	Yes	No	Yes	No

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

Other hyponyms of waving include brandish.

waving (noun)	flourish (noun)
the act of signaling by a movement of the hand	the act of waving
	a display of ornamental speech or language
	a showy gesture
	(music) a short lively tune played on brass instruments
	an ornamental embellishment in writing

waving (verb)	flourish (verb)
	grow vigorously
	move or swing back and forth
	make steady progress; be at the high point in one's career or reach a high point in historical significance or importance