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How does a brokerage firm work?
Brokerages offer you the convenience of buying and selling financial products. They are usually not exchanges themselves, but they can be. Typically there is an exchange and the broker sends orders to that exchange. The main benefit that brokers offer is a simpler commission structure. Not all brokers have their own liquidity, but brokers can have their own allotment of shares of a stock, for example, that they will sell you when you make an order, so that you get what you want faster. Regarding accounts at the exchanges to track actual ownership and transfer of assets, it is not safe to assume thats how that works. There are a lot of shortcomings in how the actual exchange works, since the settlement time is 1 - 3 business days, depending on the product (so upwards of 5 to 6 actual days). In a fast market, the asset can change hands many many times making the accounting completely incorrect for extended time periods. Better to not worry about that part, but if you'd like to read more about how that is regulated look up "Failure To Deliver" regulations on short selling to get a better understanding of market microstructure. It is a very antiquated system.