In fact, an account on a cryptocurrency exchange has a lot of sub-accounts. For each cryptocurrency, the exchange has its own sub-account: Bitcoin is stored on one, Ethereum on another, USDT on the third. But the trader sees all sub-accounts combined into a common account. It's convenient.
In order to make a transfer to another exchange, the trader needs to know the address of the account on the network through which the transaction will be processed. The account address is an analogue of the bank account details.