A democratic currency (a.k.a. democratic monetary system or democratic money) is any currency that pays an income of itself to people unconditionally and in a recurring fashion.
A society that can guarantee the payment of a Universal Basic Income of money (i.e. currency, cash, legal tender) to people is not necessarily doing so through a democratic currency.
Usually, UBI is understood as coming from government taxation. That means the currency or monetary system itself is undemocratic: it is not actually hard-wired to issue itself to people. Instead, the currency is "static," and unaware of how many people actually exist. In other words, an undemocratic monetary system has no visibility into the actual people when running its monetary policy code. Thus, UBI using existing, undemocratic monetary systems, consists of an external agent (a higher-level layer of the whole economic/financial system) actually forcing people to yield existing undemocratic, people-unaware money to a taxation pool, which is then redistributed to people to guarantee and implement a Universal Basic Income.
Democratic money is about hard-wiring Universal Basic Income directly into the currency system itself, so that there is no need for a higher-level entity to track existing money and to come up with rules regarding its collection and redistribution. Democratic money is possible with existing technology, and blockchain, cryptocurrencies, and digital money are key technological pieces of the puzzle.
Most Crypto UBI projects are based on the creation of democratic currencies.