hesitate vs vacillate

hesitate and vacillate both are verbs.

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

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

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

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

hesitate (verb)	vacillate (verb)
pause or hold back in uncertainty or unwillingness	move or sway in a rising and falling or wavelike pattern
interrupt temporarily an activity before continuing	be undecided about something; waver between conflicting positions or courses of action