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Barber = hair cuts for men (no coffee, no talking, in and out as fast as possible, nose hair, eyebrows and ear hair gets trimmed as a matter or course)
Hairdresser = hair cuts for women (very coffee, maybe even a glass of wine/prosecco, much talking, 2 hours min, scalp hair only)
Unisex hairdresser = haircuts for men and women (some talking, maybe a coffee, longer than you'd like, 50/50 on general head-based hair management)Purely anecdata, but that's where I'd put the divide.
If we exclude the trendy faux-barbers that have sprung up like wide fire:
Hairdressers generally:
A lot of which adds risk, but the appointment system would allow better risk management than a barbers queue and cab rank system, as well as likely a lower number of customers.