The last piece in the number of photons puzzle is the actual "photograph" itself.
A photograph is nothing more than a recording of photons. In the bad old days, you had film. These days you have a digital sensor.
The term ISO dates back to film. It has been co-opted in the modern digital world.
Effectively, it tells you the film's sensitivity to light. (In the modern world, digital sensor's sensitivity to light.)
The designers were well aware of the fact that light strikes the eye logarithmically so twice the ISO meant twice the speed.
Now digital sensors are basically the same but they allow going up to far higher ISO speeds than bad old film ever could.
Theoretically, going to higher and higher ISO's means that you are effectively increasing the "number of photons". However, practically it doesn't work that way.
That's for a future post though.
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