Brothels normally have a number of girls working at the same place trying to persuade the customers to move from the public zone like the bar to the rooms. There is no madam introducing you the girls and if there is some advertising it will promote the place, not the girls. They will have to do all the work and they work for the volume of customers. So, in theory, the price is discounted when compared to flats or agencies, but it is normally more expensive than for street walkers and many indies. However, top brothels could be very expensive. In the UK, brothels are illegal and only one girl could work at the same place. However, in other countries could be dozens of girls working and competing for the customers under the same roof. The largest ones could have up to 100 girls working together.
A massage parlor is a hidden brothel. They offer massages as they are legal, frequently with a happy ending and sometimes very happy ending.
A flat is a place with several girls working there, normally a madam introduces you the girls, you chose one, and you directly move to the room with the girl that you have chosen. In a presentation, the madam calls the girls, they come to you one by one, tell you her "name" and then leave. When the last one has left the madam will ask you who you like to sleep with and how long you want to stay. Sometimes, there is no madam and one of the girls will introduce you to the rest.
An agency use to be an intermediary between you and the girls you called the intermediary and they provide you the girl. At the beginning, they were meant to be for outcalls only but, currently, most of them provide incalls as well and many times they look like a flat. However, the best top agencies have detached operations. So, the office and the flat for incalls are in different places, and it won't be shared by two or more girls at the same time, just by you and the escort.
Indies are independent escorts, freelancers, that don't work for anybody else. So they keep all the profits of a service, but also all the risks and expenses. The brothels, massages, agencies and flats normally split the profits with the girls, and in return the offer them a place to work, safety and promotion.