To make things even more convoluted, anybody can issue their own euros (for example), simply by writing an IOU. This is effectively what banks do, making their version of the currency (theoretically) less valuable than euros issued by the ECB (sovereign money), simply because the private banks are less reliable issuers.
Both yes and no. I could write an IOU for a thousand euro's on one piece of paper, and write a 1000 euro's on another piece of paper, but I doubt anyone would accept the latter. But yes, this is what banks do with fictional reserve banking. They credit one account with a 1000 euro's, and debit another account for a 1000 euro's at the same time.