Tokens can be stored digitally and traded like NFTs, albeit with a face value. Tokens can be bundled together in any combination to transfer particular sums of money. Special tokens can also be held and traded separately, like antique or special-edition coins: face value if you want, collectable if you want.
Each token has a unique serial number (like any digital object, which can be distinguished by a unique private/public keys etc.) The network can track serial numbers to owners, and/or track whether the holder of the object's private key sets a value associated with the token to "locked" or "unlocked." Locked serial numbers cannot be transferred to a new owner without the original owner's private key. Unlocked serial numbers can be transferred to a new owner without the original owner being further involved.
If you print the token, including its serial number (which can be represented as a number and/or a QR code) and lock the token on the network, then the printed tokens cannot be traded, meaning even if someone is holding the printed object and has access to the serial number, they cannot change the object's network status. However, if the object is set to "unlocked," then anyone who inputs the serial number can opt to become the new owner, and the old owner loses access.
In this way, you can walk around with a wallet full of printed locked tokens, and if your wallet is lost or stolen your money is still safe. You are the only one who can transfer the network status of the objects. Anyone who scans them will find they are "locked" - useless. However, if you find an unlocked token in the street, you can register it to yourself; you are now the only cryptographic owner of that object.
Just like with fiat paper money, you cannot tell with cryptographic certainty by looking at it whether it is unique/real or counterfeit. Maybe you use a special pen that might work to reveal counterfeits. But with digital cash, you can scan it or enter the serial number into an app, and if the serial number comes up as valid and unlocked, it is as certain and secure as anything humanity has invented to date that the object is unique, real, secure, and trustworthy. Sweep it or register it to yourself, and you but no one else will have its new private key. Once it's registered to you, do what you want with the paper - keep it in case you want to unlock and spend it again; throw it away and re-print it another time; etc.