hairdresser vs barber

hairdresser and barber both are nouns.

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

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

Other hyponyms of hairdresser include coiffeur, coiffeuse, tinter.

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

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