A Central Bank is a private institution of a country responsible for interbank trading, monetary transactions, financial stability and economic development.

A Central Bank is setting inflation targets, attempting to control the lending and borrowing between financial institutions in order to influence deflation/inflation.

A Central Bank is a public institution of a country responsible for interbank trading, monetary transactions, financial stability and economic development.

A Central Bank is a government ministry responsible to handle inflation. 

A Central Bank is setting allowed inflation, and controls financial institutions holding that monetary deflation/inflation.