Cryptocurrencies are a form of digital money, but what we normally understand as digital money is represented in fiat currency. For instance, prepaid cards, virtual credit cards and other forms of digital money are simply fiat money deposited into some account under a traditional banking institution. Parents, for instance, can load up their children's cards with some amount which is withdrawn directly from their checking account. This is all traditional money with some digital convenience.
Cryptocurrencies on the other hand are a completely different animal. They're digital but that's the only thing they have in common with traditional digital money. Cryptos are decentralized and peer to peer. There is no banking institution involved in cryptocurrency transactions. The integrity of a cryptocurrency transaction depends on distributed consensus algorithms that are either based on stakes or on work, such as PoW and PoS and the verification activity we've come to know as mining or staking. Digital money does not depend such distributed algorithms at all, on the contrary, a central baking institution does all the bookkeeping. Every digital money transaction is checked against a central server which indicates whether you still have the amount requested in credit or not.
The concept of digital money goes back to the early 1980's. Credit cards were all the rage but they required a physical machine and the cardholder's signature on a piece of paper. Credit card bills were assembled by hand at central facilities run by American Express, VISA and MasterCard and the likes. Early digital money ideas such as Digicash did not require the plastic at all. Years went by and for one reason or another, Digicash never took off. With the explosion of the WWW in the 1990's, Elon Musk and his Paypal payment system became the online norm for the exchange of money. Early on Paypal was very liberal, it was trivial to open an account and exchange money using it. Anti terror laws were not as rigid and it was fairly easy to simply open up a Paypal under whatever name and start exchanging goods and services online. Today Paypal is fully regulated and very strict. For years Paypal and similar payment systems were the closest we got to digital cash.
In 2009 Bitcoin revolutionized the concept of digital money. It solved the double spending problem and provided a working solution to fully decentralize the transfer of value that required zero trust on any party involved. It was a revolutionary step forward which sparked the entire cryptocurrency industry as we know it. Miners entered the proof-of-work game for their own interest, not out of altruism: the system had found a way to offer rewards such that people were willing to verify transactions voluntarily, against a block reward for every solved block. No previous system, like HashCash for example on which Bitcoin is based, had found "the carrot" to get people to mine transactions for the community - only by offering a financial reward did Bitcoin also solve the mining incentive problem.
Therefore the main difference between earlier concepts of digital money and cryptocurrencies is mainly decentralization. Digital money must represent some value stored somewhere and is usually centralized and verified by some form of banking institution where credit is provided, either from a checking account's balance or some credit amount. Cryptocurrencies on the other hand are fully decentralized and do not depend on the verification from a single point, but instead depends on distributed consensus which is algorithmically determined by peers in the same network. Cryptocurrencies fall under the concept of digital money, but they're more sophisticated forms of digital money that are not necessarily tied to any particular fiat currency (with the exception of Tether and cryptos designed specifically to be tied to fiat money).
While decentralization is taken for granted now, 9 years on from the revolutionary concepts introduced by Satoshi Nakamoto's famous whitepaper, it is still the main differentiator between real cryptocurrencies and legacy digital money projects that are not decentralized. In fact, the consensus mechanism in Bitcoin can be deployed by private institutions to be used as a distributed database, without the need for the financial concept of a crypto currency (blockchain applications). It is only when the concepts in Bitcoin are assembled together in the creative way in which Satoshi did it, that the true magic happens.
Bitcoin is an evolution from previous digital money projects. HashCash, for example, attempted to attribute a work value to each email message so that spam would become financially unfeasible. This proof of work system deviced by Adam Back forms part of the backbone of the Bitcoin system. There still remained the double spending problem and a rewards system for people to voluntarily participate in mining. The incentive problem was solved by the concept of a value token, a "coin" that would be paid out to everyone who mined transaction. And the double spending problem would be solved by brute force: proof of work would make it more expensive to defraud a Bitcoin block than to mine one in legit fashion, thus providing a way to make fraud more expensive than the potential reward per block. This decentralized mechanism then became what we now know as Bitcoin, and the rest is history.