hairstylist vs barber

hairstylist and barber both are nouns.

Word	Noun	Adjective	Verb	Adverb
hairstylist	Yes	No	No	No
barber	Yes	No	Yes	No

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

Other hyponyms of hairstylist include coiffeur, coiffeuse, tinter.

hairstylist (noun)	barber (noun)
someone who cuts or beautifies hair	a hairdresser who cuts hair and shaves beards as a trade

hairstylist (verb)	barber (verb)
	perform the services of a barber: cut the hair and/or beard of