Analog/digital and continuous/discrete are two independent axes — not two names for the same thing

‘Analog’ means ‘bearing an analogy to something’ — a mic signal is an analog of air pressure changes. ‘Digital’ means ‘represented by numbers.’ These describe what the signal represents, not its temporal structure. ‘Continuous’ means values that flow without gaps; ‘discrete’ means values sampled at a fixed rate. The confusion arises because analog is almost always continuous in practice, and digital audio is always discrete. But analog can be discrete (Bucket Brigade Devices store discrete analog voltages in capacitors), and a digital signal transmitted over a wire is carried by a continuous flow of voltages. The useful distinction for audio is continuous vs. discrete, not analog vs. digital.

Examples

A Bucket Brigade Delay (BBD) pedal samples analog voltages at a fixed rate — discrete analog. A digital audio stream on an AES-EBU cable is digital values transmitted as continuous voltage swings — both digital and analog. A DAC’s output is an analog of the digital number, but also of the music.

Assessment

Is a Bucket Brigade Delay circuit analog or digital? Is its signal continuous or discrete? Justify each answer, then explain why the question ‘is this analog or digital?’ is less useful than ‘is this continuous or discrete?’