Analogue comes from computing.
"A Chronology of Analogue Computing" article in The Rutherford Journal
The word ‘analogue’ was first used as a technical term during the
1940s, and referred specifically to a class of computing technology.
Today, the word enjoys much wider usage, typically conveying
continuity. For example, engineers will discuss analogue and digital
signals, and musicians decide whether to record their work on analogue
(continuous) or digital (discrete) media.
Analogue computing emerged during the nineteenth century and became a
mainstream computing technology during the early twentieth.
The word analogue has been used because the electric signal, for example, in analogue telephone line, is transmitted in a way that the voice vibrations correspond to electric signal fluctuation. In other word, the electric signal 'imitates' the voice.
In digital transmission, voice is coded into bytes, then is decoded with special protocol.
Another example is radio vs Morse code. Radio directly (by analogy) transmits the voice with electric signal variation. Morse code transmits only combinations of dots and dashes that are decoded by a trained person. So we can call Morse message digital because the concept is the same coding and decoding rather than an electric analogy of physical phenomena.
So the word analogue is used to reflect the concept when some physical phenomenon is converted into its electric signal analogue.
The word digital is used when a phenomenon properties are coded, then decoded.
Here are a few examples and articles to explain the difference between analogue and digital concept:
The basic difference between analog and digital technology on howstuffworks.com
Analog vs. Digital with explanation and comparison chart on diffen.com