The accounts offered by banks differ in the facilities offered, the tenure of deposits, and the rates of interest. Most accounts can be divided into one of the following categories:
Savings accounts: These accounts allow customers to deposit funds and earn an interest on their deposits and there is usually no restriction on withdrawals. Most saving accounts do not allow the account holder to write checks. The interest rate in saving accounts is also quite low.
Checking accounts: These accounts allow the account holder to deposit funds and make transactions like transfer of funds to others and writing checks. The kinds of transactions that can be made, how often they can be made and the charges involved vary for different types of checking accounts. Most checking accounts are non interest bearing.
Money Market Deposit Accounts (MMDAs): Deposits made in these accounts earn a higher rate of interest but this is accompanied by a minimum amount that has to be always maintained in the account; the types and frequency of transactions that can be made is also restricted.
Certificate of deposits: These accounts require account holders to deposit funds for a long duration of time. The interest rate offered is the highest in this type of account and increases as the time period for which the account created.
Banks offer multiple types of accounts with a multitude of different interest rates per bank, per account, per amount of money deposited or invested, per whether the bank is insured by the Federal government and per number of accounts an individual already has at a particular bank.
That being said, the standard types of accounts are checking accounts, savings accounts and money market accounts. The most important things to look for when opening an account are that the bank is an FDIC institution and that you earn compound interest.
I hope that helps.