Booth (or chair) rental is a common arrangement where a stylist, barber, or nail/lash technician pays a salon owner a flat rent, weekly or monthly, for access to a chair and shared facilities, while operating as their own independent business rather than a salon employee.
As a renter, you're generally responsible for your own supplies (beyond what's negotiated), your own booking system, your own clients and pricing, and critically, your own taxes and insurance, nothing is withheld for you the way it would be as an employee. A written booth rental agreement should spell out rent amount and frequency, access hours, what's included (backbar product, laundry, front-desk booking support) and what isn't.
Because you're running an independent business inside someone else's space, keeping clean separate records, your own invoices, your own expense tracking, matters even more than for a typical freelancer, since a booth renter relationship that looks too much like employment can create misclassification risk for the salon owner.