This post is not as clear as it should be. Sorry. It's because my head is not very clear either. I wrote this to try to get my head clearer.
An imaginary country uses 7 different media of exchange, issued by 6 different banks.
There is one alpha bank, and 5 beta banks.
The alpha bank issues one medium of exchange printed on paper, and a second medium of exchange printed on silicon.
The 5 beta banks each issue one medium of exchange printed on silicon.
Anyone can use the paper issued by the alpha bank. Anyone can use the silicon issued by the beta banks. But only the banks can use the silicon issued by the alpha bank.