One key difference between a government issued currency and a distributed cryptocurrency is that the former is based on a promise and the latter is based on trust.
A government issued currency is based on the promise [1] given by a state that this money must be accepted by everybody else. Everyone can enforce his rights by law.
A distributed cryptocurrency is based on trust given mutually by the users. The trust relays on the circumstance that no significant number of participants will abandon their precious investment may it be acquired through mining or purchasing of coins.