It's probably just a semantic argument. Governments enact legislation that gives them the authority to issue currency via central banks and tax ie control the supply of public and private surplus/deficits in the market. Governments don't require the consent of any one to do this it is instituted by force. A private currency would require the consent of consumers, it would be entirely voluntary. From my reading CBs are addressing the issue because FB's Libra has put the wind up them. The thought that private entities can issue currencies that enable individuals to transact with each other using a medium that is free of inflation and the machinations of central planning policies (which means central bankers become redundant), and that individual may have a preference for such currencies is challenging the authority of the State. That is one form of private currency. Businesses could also issue their own credit notes, of course they would have to be reputable and have some form of collateral as backing for the currency.