Both the State Government and the Federal Government have authority to grant bank charters; thereby creating “THE DUAL BANKING SYSTEM”.  A bank can choose to have a national charter or a federal thrift charter (with the Office of the Comptroller of the Currency).  There are no major differences in powers between State and Federal charters.

Generally, the business of banking involves financial services such as car loans, home mortgage loans, business loans, checking accounts, credit card services, certificates of deposit, and individual retirement accounts, and facilitating the movement of funds.

Your bank is probably insured by the Federal Deposit Insurance Corporation (FDIC), an independent agency of the Federal Government. Almost all United States banks and savings associations have their deposits insured by the FDIC. The agency is named receiver if a bank fails. It is also the primary federal regulator of state-chartered banks that are not members of the Federal Reserve System.

All FDIC-insured banks must meet high standards for financial strength and stability. The FDIC, with other federal and state regulatory agencies, regularly reviews the operations of all insured banks to ensure these standards are met.  Government regulatory agencies do not release their ratings on the safety and soundness of banks and thrifts to the public.  

Do I Need to Know If My Bank Is Healthy? (Links off-site to the FDIC)

Other Resources:

FDIC Deposit Insurance Resources