In the US, for instance, the federal government includes the President and Congress at the top of the hierarchy. Congress authorizes taxing and spending measures. Below this level are the Treasury and Federal Reserve (central banking system).
The Federal Reserve system is a separate 'arm of the government' altogether. Technically, it's not even part of the government, as it's privately held (though many central banks around the world are held directly by the government.) The Federal Reserve is supposed to operate independently of political pressure, thus its separation from the rest of the government.