Private money. Patterson, NJ, Bank Note
Stonington Bank, Connecticut.
"The Federal Reserve is a private bank - given a charter by the US government. "
This is a contradiction. No person, or entity, given 'charter', like as in some days of French Royalty, is private. As is not the Federal Reserve. It is what is known today as 'GSE', government sponsored entity. Like, Fannie, or Freddie. In other words, an abortion to republican government. Not that that has mattered much the last hundred years.
Banks can still (and still do) issue notes. See HSBC Bearer Notes. The question is which entities have the right to "increase the money supply" or create money in the first place.
Anyway, I agree that the Federal Reserve is a bastardization of government and industry, ala Freddie and Fannie, only more insidious on account of the Federal reserve isn't as accountable to the people as Congress is. My simplistic explanation is that where Congress used to issue money in an accountable fashion (and has the authority to do so without entering into a borrowing/debt agreement with a bank), now it hides behind "The Federal Reserve," and promises to the Federal Reserve to repay MORE than it borrows from the Federal Reserve, with the difference to be made up by tax receipts.