Crypt-currencies, like Bitcoin, are decentralized but not distributed. There remains a logical central authority, but no single holder of that authority.
A fully distributed currency would have multiple issuing parties with exchange agreements between each other. This opens the door to time-limited self-issued credit or currency.
This allows for local currencies to be used for local only transactions with the possibility of exchanging one local currency for another to broaden the usability, including worldwide.
A given transaction is with the issuing authority and therefore sub-second. Credit is issued as fixed unit amounts or coins that are not divisible. Once a given unit returns to the issuer it’s id is extinguished and so it any traceability. Semi-trusted offline exchanges become possible.
Client software wallets can manage and broaden the exposure to loss by holding value with multiple issuers.
Transactions occur with unique keys exchanged between the parties. Digital signatures allow for verifiable data to be kept by all parties.
Using the Matryoshka protocol, transactions are private, untraceable, and no evidence is exposed that one ever takes place.
Issuing and managing of transactions is cheap and does not require a mining process. Money is made by the producer of the product or service, not the money-changer.