vacillate vs waver

vacillate is not a noun while waver is a noun.

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

As verbs, vacillate and waver are synonyms defined as:

vacillate and waver: move or sway in a rising and falling or wavelike pattern

Other synonyms of vacillate include fluctuate.

As verbs, waver is a hypernym of vacillate; that is, waver is a word with a broader meaning than vacillate:

vacillate: be undecided about something; waver between conflicting positions or courses of action
waver: pause or hold back in uncertainty or unwillingness

Other hypernyms of vacillate include hesitate, waffle.

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

vacillate (verb)	waver (verb)
move or sway in a rising and falling or wavelike pattern	give off unsteady sounds, alternating in amplitude or frequency
be undecided about something; waver between conflicting positions or courses of action	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