What's gain?
The term "gain", which is output divided by input, without explication, is ambiguous. You can have gain where the input and output units are the same: current gain, voltage gain, power gain, etc. You can have AC gain and DC gain. At higher frequency, you can have voltage gain margin at phase crossover. Those gains are dimensionless.
You can have gain with different units: conversion gain is an example, where the numerator is voltage and the denominator is electrons. The dimensions of conversion gain is voltage over charge. One gain of a transconductance amplifier has the units of current over voltage.
Circuits can have several different relevant gains. The voltage gain of a source follower is less than one, but the current gain is more than one, and so is the power gain.
I have designed many systems with mixed analog and digital processing. I referred to manipulations of signal level as gain, whether that gain was achieved through analog amplification or digital computation. But maybe I and the folks I worked with were outliers. I know we referred to raw integer digital representations as "counts", and I don't see many using that terminology when describing cameras.
And, by the way, when one says that a circuit has some kind of gain, that doesn't mean it amplifies. Gains can be less than unity.