Digital currencies and cryptocurrencies differ from each other in how they operate.
_There must be a server for the whole system to be maintained. That means authorities can control the currencies by controlling the server.
_From the security perspective, The server needs to be protected from hackers.
_Everything operates on the blockchain, which can be considered the same as digital currencies 's server, but it doesn't run on 1 hard server . It runs on hundreds of thousands of computers that miners turn on for block reward. Each of these computer runs the same thing on it simultaneously, and when all of those computer (or a majority of them) reach a consensus, that's the blockchain.
_Because there's no server, governments can't control the blockchain or shut it down (with the same reason why copyrights holders can't shut bitTorrent down, or why people can't kill SkyNet in the Terminator series). In the case governments want to shut the blockchain down, with just 1 single of the hundreds thousands computers, located around to globe, running the blockchain, survives, the chain survives.
_From the security perspective, the only way to "hack" a block chain is to hack 51% of ALL THE COMPUTERS running it AT THE SAME TIME (within the same block, which typically ranges from a few seconds to a few minutes). That's why if the chains is large enough, it's theoretically impossible to hack the blockchain.
Edit: (further explaining the "hacking")
By hacking the blockchain, I mean the same as controlling a server that run something and change the datas. For example, the hacker can set the balance of his account to 1 million dollars. In online banking system, or digital currency server, it can be done by hijacking the server. As for cryptocurrencies, the same thing can be done by controlling 51% of all the hardware running the blockchain, and it have to be achieved within the same block on the chain (a few secs to mins), because when when the new block is mined or forged to the chain, all previous block is encrypted, which is impossible to decrypt within a a few seconds (block-time for the following block).