The cashless society is one of my favorite research topic and this a concept similar to the barter economy where the paper currency or the cash was simply absent. This case depicts the shift to another level in the economy and this can be the next stage at which the governments will either not print the paper currency or the people might not accept it but this can only be possible if all the people around the world use the technology which I do not think is possible until the next five decades.
In cashless society there is same amount of money (no change) but payments are done by debit cards and credit cards (digital payments). No paper currency and coins are used in the economy.
Bitcoin may be broadly considered part of digital money. However, it is a world different from the digital money that you mentioned in that they are not cryptocurrencies. When you mentioned debit cards, paypal, alipay, bankwire transfers, online payments, etc, you were basically referring to fiat money. Fiat money developed into a cashless form of money with these methods but then they are still fiat money and are still very well under the sanction of the banks.