Hairstylist:

A barber (from the Latin barba, "beard") is someone whose occupation is to cut any type of hair, give shaves, and trim beards. In previous times, barbers also performed surgery and dentistry.[1] In more recent times, with the development of safety razors and the decreasing prevalence of beards, most barbers primarily cut hair. Some hairdressers consider the term derogatory.[2]
Although many barbers may still deal with facial hair when requested, in American and Commonwealth culture most barbers specialize in the simple cutting of men's hair. They do not generally offer significant styling or 'fancy' haircuts when compared to hairdressers working in hair salons.
The place where a barber works is generally called a barbershop, or simply the "barber's".
A hairdresser is a universal term referring to someone whose occupation is to cut or style hair in order to change or maintain a person's image. This is achieved using a combination of hair colouring, haircutting and hair texture techniques.