What is a Banknote? Does a banknote have to come from the government?

A piece of paper money, and yes it does

A banknote (often known as a bill, paper money, or simply a note) is a type of negotiable promissory note, made by a bank, payable to the bearer on demand. Banknotes were originally issued by commercial banks, who were legally required to redeem the notes for legal tender (usually gold or silver coin) when presented to the chief cashier of the originating bank.