hesitate vs waver

hesitate is not a noun while waver is a noun.

Word	Noun	Adjective	Verb	Adverb
hesitate	No	No	Yes	No
waver	Yes	No	Yes	No

As verbs, hesitate and waver are synonyms defined as:

Other synonyms of hesitate include waffle.

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

Other hyponyms of hesitate include dwell on, linger over, boggle, hover, linger, hover, oscillate, vacillate, vibrate, falter.

hesitate (noun)	waver (noun)
	the act of moving back and forth
	the act of pausing uncertainly
	someone who communicates by waving

hesitate (verb)	waver (verb)
pause or hold back in uncertainty or unwillingness	give off unsteady sounds, alternating in amplitude or frequency
interrupt temporarily an activity before continuing	sway from side to side
	move or sway in a rising and falling or wavelike pattern
	move back and forth very rapidly
	move hesitatingly, as if about to give way
	pause or hold back in uncertainty or unwillingness
	be unsure or weak