Do all accounts serve the same function? why or why not?

No, accounts serve the purpose that their owners choose. They do not have the same function.

>>>Accounts are financial records of an organization that register all financial transactions, and must be kept at its principal office or place of business.
In accounting, it means the chronological record of changes in the value of an entity's assets, liabilities, and the owners' equity

In banking,it means continuing financial relationship between a bank and a customer,whereby deposits and debts are held and processed within a framework of established rules and procedures.