Your question doesn't actually make sense, in that FED and FRS both refer to the Federal Reserve System of the United States. Did you intend to contrast different organizations?
The Federal Reserve determines monetary policy for the United States, an extremely important function, as the issuance of too much money into the economy will spur inflation, while tightly restricting the flow of money can cause a recession.
In addition to its paramount responsibility for determining monetary policy, the Federal Reserve System is also the regulatory agency for state-chartered banks that are part of the Federal Reserve System, bank holding companies and for foreign banks operating in the United States. It is one of four regulatory agencies responsible for different categories of banks. Another bank regulator, The Office of the Comptroller of the Currency is responsible for oversight of federally-chartered, or national, banks. The Federal Deposit Insurance Corporation conducts oversight of all banks that participate in its insurance program designed to protect individual depositors. In practice, the FDIC focuses its regulatory responsibilities on FDIC-insured banks that are not members of the Federal Reserve System.
Finally, there is the National Credit Union Administration that, as its name suggests, is the supervisory agency for the nation's credit unions. Until recently, there was a fifth regulatory agency, the Office of Thrift Supervision. The OTS was dissolved with the passage of the Dodd-Frank Act, which dispersed its functions among the other bank regulators.
Each of these agencies serve and oversee the banking industry.