A barbershop caters more for men - cutting hair and shaving. Although shaving occurs less now. Usually women do not go to barbershops. Some women can be barbers but it is uncommon. A beauty shop caters more for women and girls and offers a much wider range of services. Services include cutting hair, bleaching , tinting, facials , nail trimming and painting. Men can go to these shops but it is uncommon. Men and women can be the owners of this sort of shop.

Not much, it's a gender role thing. Like the idea that men go to barbours and women go to beauty shops. Now that's not really true that's just the general stigma that occurs. It just depends on who's running the place and how they present their service.