Many online brokerages do not limit their customers to just online stock trading. Full-service brokerages offer banking services including checking accounts, savings accounts, credit cards, mortgages, and more with deposits of up to $250,000 backed by the FDIC. Bank of America (Merrill Edge) and Chase (Chase You Invest Trade) are two examples of banks that also offer online trading.
For online platforms, websites give the user options and availability of the stock he wishes for, across all the platforms available. If he places an order, it gets stored in a database. After the confirmation of the trading account and payments, the order gets forwarded and the user gets his stock, in the form of money, transferred to his trading account.