The distinction is in how they are interpreted. A digital signal is analog in nature, but is viewed as having only two states: high or low [that can be voltage or current].
Another way of looking at it is: with analog, the voltage or current levels carry the information, as in an audio signal. These levels translate directly when applied, as an audio signal to a speaker.
Digital, carries the information as a set of numbers, encoded as ones and zeros. A digital signal must be decoded before it is physically applied, If you feed a digital signal directly to a speaker, you will get incoherent noise, even if the signal carries the audio information in digital form. This information must be extracted using something like a DAC (Digital to Analog Converter) before it is applied to the physical.
BTW: "zero" and "one" in a digital signal is arbitrary and can be encoded as "high" equals 1 and "low" equals 0 or vice versa. And it's not even zero volts and the maximum voltage. Each logic technology has it's own rules for interpreting ones and zeros. For TTL input signal levels anything between 0.8V and 0.0V is considered a zero, and anything between 2,2V and 5.0V is a one. For CMOS, where VDD is 10V, a zero is anything below 3V and a one is 7V to 10V. ECL considers -1.75V to be a zero and -0.9V to be a one. And, it's even possible to encode more than just two states. Binary is not the only digital base that can be used.
So, digital is analog levels interpreted as digital states.