The zeta-function machine depended on measuring the moment of a collection of rotating wheels.
This physical quantity was to be the 'analogue' of the mathematical quantity being calculated.
On the other hand, the binary multiplier had depended upon nothing but observations of 'on' and 'off'.
It was a machine not for measuring quantities, but for organising symbols.
In practice, there might be both analogue and digital aspects to a machine. There was not a hard-and-fast distinction.
The Bombe, for instance, certainly operated on symbols, and so was essentially 'digital', but its mode of operation depended upon the accurate physical motion of the rotors, and their analogy with the enciphering Enigma.
Even counting on one's fingers, by definition 'digital', would have an aspect of physical analogy with the objects being counted.
However, there was a practical consideration which provided the effective distinction between an analogue and a digital approach.
It was the question of what happened when increased accuracy was sought.