There was a time when there were banknotes issued by private banks. In fact, there are still some countries which allow this, such as Scotland, Northern Ireland, and in China Hong Kong still has banks that issue private notes. In the United States, the issues of banknotes started early on with the Colonies issuing notes, which naturally converted to state issues. After the Revolutionary War, Federal notes depreciated greatly in value, and the term "Worthless as a Continental Dollar" was prominent. As a result of the public losing faith in Federal dollars, private banks, railroads, and even businesses began issuing banknotes. In fact, according to the Professional Currency Dealers Association, there were well over 1,600 banks in the United States which issued over 300,000 varieties of banknotes.
This was all well and good, but there is the inevitable question of what happens when you try to spend a banknote issued from the state of Massachusetts in Georgia? And what happens when a local bank in New Jersey issues a note and you want to go to Chicago? Well you'd want to change your notes over to federal issued notes, or better yet, change them into coins, which were issued federally and were accepted all over. Just because it was a banknote, it wasn't guaranteed to be worth anything to anyone other than the issuing bank, so the farther you got away from the area, the more your locally issued banknote could be discounted, as the receiver was unfamiliar with the issuer, and to exchange it was a bit of a pain. But the fact is, most people didn't travel very often back then, and when they did, they didn't go too far, so these notes circulated pretty well. Several of these notes exist, with many of them being un-issued remainders that were left in a vault somewhere. Those that were issued are often beat up from use. The US Government put an end to Privately issued banknotes in 1863, and they bacame known as "Broken Bank Notes", "Wild-Cat Notes" or, more typically, "Obsolete Banknotes."