What is the opposite of "digital"?
Analog, meaning non-quantized (i.e. capable of smooth variation), has become the word most often used to express a contrast to digital by default, even in cases where it may not be strictly appropriate. (It often forms the modifier in a retronym, a new word or phrase used to distinguish the original version of something from a newer rival.)
Analog probably became the word of choice after its use in analog recording (as opposed to digital recording technologies such as CDs) and analog watch (as opposed to digital watches). In both cases it was appropriate because the smoothly varying analog signal was a direct contrast to the quantized digital experience.
In this particular case, even non-digital money is quantized, but analog at least has the advantage of being readily understood.
Analogue - Relating to or using signals or information represented by a continuously variable physical quantity such as spatial position or voltage.
Digital - (of signals or data) expressed as series of the digits 0 and 1, typically represented by values of a physical quantity such as voltage or magnetic polarization.
Analogue uses Continuous Variables whilst Digital uses Discrete. Analogue is more physical than digital, like watches. Analogue watches use spatial position (a continuous variable) whilst Digital watches use 0s and 1s to show their information, which is discrete, and not continuous.