That cleavage is de facto, not de juris. From the Federal Reserve Act, Section 10.6 "Nothing in this Act contained shall be construed as taking away any powers

That cleavage is de facto, not de juris. From the Federal Reserve Act, Section 10.6 "Nothing in this Act contained shall be construed as taking away any powers heretofore vested by law in the Secretary of the Treasury which relate to the supervision, management, and control of the Treasury Department and bureaus under such department, and wherever any power vested by this Act in the Board of Governors of the Federal Reserve System or the Federal reserve agent appears to conflict with the powers of the Secretary of the Treasury, such powers shall be exercised subject to the supervision and control of the Secretary." The constitution gives Congress the power to create money, then congress delegated this right to Treasury by passing the legal tender act in 1862. This right has been delegated to the Federal Reserve system so they now issue Federal Reserve Notes, but is subject to the supervision and control of the Secretary of the Treasury as specified in 10.6 But in practice we give the Fed leeway so as to not be seen as interfering in money creation and reserve policy because that is what financial markets demand and is what the general class of educated and influential people believe is the best approach.