Money is just a promise. Anyone can create those. Which should be quite obvious. When you go to work to, as we literally say, make money, your employer is making a promise that in exchange for you work you can take something of some defined value later. Later, you will take that promise and turn it into something of value, such as food. Once spent, the money is destroyed. The promise is no longer valid. The deal is done.
Currency is a promise to a particular entity, such as a central bank. A central bank will loan you something of some value, you equally promise to give them something of equal value (we'll ignore interest for simplicity) back at a later date. Indeed, only the central bank can accept promises made to the central bank. If you accepted a promise on behalf of the central bank, without explicit authority, then you are quite right that trouble is coming your way.
Because there is a trust component required in promises, often promises made – such as the promise of your employer to feed you later – will be backed by a promise to the central bank. The central bank has a military to send if someone really tries to play nasty with promises made, so that carries a lot more trust than if you and I wrote up our own 'IOU'. This may be why you see money and currency as being one and the same. Often they are, but not necessarily so.
Accounting is simply for keeping track of promises. That's why we invented it. You don't need accounting for barter. It is the promises that necessitate accounting in order to keep track of what promises are outstanding and what are fulfilled. A bookkeeper doesn't create money per se, but they certainly account for money created and destroyed by the entity they are bookkeeping for.