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A central bank is a public institution, generally controlled or managed by the national government, that has the primary role of controlling a country's money supply, interest rates, and overseeing the financial system. Examples of central banks include the Federal Reserve System in the United States, the European Central Bank, and the Bank of Japan.

A commercial bank is a financial institution that provides various financial services to individuals, businesses, and other organizations. They primarily accept deposits from customers and provide loans. Examples of commercial banks include Bank of America, Citibank, and Wells Fargo.

The main functions and purposes of central and commercial banks differ in several ways: 1. Money Supply Management: Central banks oversee and control the money supply through monetary policy tools such as open market operations, setting reserve requirements, and setting interest rates. On the other hand, commercial banks create money through the process of lending and accepting deposits but do not have direct control over the money supply. 2. Interest Rate Control: Central banks set the benchmark interest rates that influence the market, thus affecting the cost of borrowing and the availability of credit in the economy. Commercial banks follow the rates set by the central bank and set their own rates for lending and deposits based on market conditions and risk factors. 3. Lender of Last Resort: Central banks can act as lenders of last resort to provide liquidity to institutions facing financial difficulties. Commercial banks, on the other hand, need to rely on their own resources or borrow from other banks or the central bank to cope with a liquidity crisis. 4. Financial System Stability: Central banks play a critical role in ensuring the stability of the financial system by regulating other financial institutions, implementing macroprudential policies, and managing systemic risks. Commercial banks, however, focus on their own profitability and risk management, making them potentially more susceptible to financial crises.

Central banks are generally owned or controlled by the national government and are usually independent from political influences to ensure sound and stable monetary policies. Commercial banks, on the other hand, are mostly privately owned and can be influenced by shareholders and market pressures. In conclusion, a central bank is primarily responsible for controlling the money supply, interest rates, and maintaining the stability of the financial system, while a commercial bank provides financial services to individuals and businesses and operates under the regulations set by the central bank.