Central banks control monetary policy and also may be lenders too. Associated terms are currency boards and monetary authorities.
A monetary authority usually will control monetary policy.
The mandate of these organizations is usually price stability and low inflation.
Central banks may be privately owned. For example, the Fed Reserve in the USA is private.
The Bank of Japan has shares and also buys securities. It has reported gains of 141 billion dollars.
“A central bank is a financial institution that is responsible for overseeing the monetary system and policy of a nation or group of nations, regulating its money supply, and setting interest rates.”