Chair Rental, also known as booth rental or weekly fee, is when you pay a monthly or weekly rental fee to the barbershop owner. You get to use the barbershop's chair to see clients and you can keep any money you earn. This is a more independent model of business where you operate your barbershop within a preexisting establishment. You can also take rental space for barbers through https://signaturesalonpro.com/.
Commission entitles you to a percentage of your total earnings in a barbershop. Commission agreements can range from a 70-30 split up to a 40%-60 split. Let's say you make $100 in a single day. You would split your 70-30 split and keep $70 while giving $30 to the barbershop owners. You would split $40 with the owner and keep $60. Another example is if you make $180 per day and are on a 50-50 split. In this example, each person gets $90.
You would be considered an employee who works for a barbershop, rather than self-employed like when you rent a booth or chair in an established shop.
You will start as a barber on a commission. Once you have a steady clientele, you can move to rent a chair/booth. This progression is traditional, but some barbers rent their entire careers while others work on a commission.
It all depends on your personal preferences. You will need to adapt to the preferences of barbershop managers or owners. This is especially true in smaller barbershops, which don't usually rent chairs.