Coining is a process whereby the owner of coinable metal asks the "coining" authority to convert the form of that metal from its current form into one of several standardized coins. "Issuing currency" (i.e., creating from nothing a medium with the capacity to discharge "current" obligations) requires the force of the state. Not only does Congress have no constitutional authority to do this but there is also an implied prohibition against it. Namely, states were expressly prohibited from "emitting bills of credit" (i.e. issuing currency in the parlance of the day). If the states had no such right, they could hardly have ceded such a function to the Federal Government.
However, there was no bank named "The Bank of the US" nor was ANY bank ever empowered to issue currency prior to the Federal Reserve. Indeed, those who foisted it upon us did so based on the fiction that we needed a lender (i.e. money creator) of last resort.