Steve Keen has a summary of what money is and how it is created here:Augusto Graziani, the Italian monetary circuit theorist, and gives an interesting, if perhaps a little idiosyncratic, perspective on what money is and the nature of a monetary production economy.
I think the whole discussion would benefit from distinguishing (1) high-powered money from (2) credit money. Any private-sector agent can create credit money, including negotiable bills of exchange, negotiable promissory notes, negotiable cheques, or bank money. The trouble is having your credit money (which is simply a promise to pay in a higher money that can finally extinguish debt at a later date) accepted as payment in a transaction, because that money creates a debt/credit relationship that almost always must be extinguished by high-powered money. High-powered money can be either (1) commodity money or (2) state-issued fiat money.
As an aside, one of Graziani’s most important books was The Monetary Theory of Production (Cambridge University Press, Cambridge, 2003).