Originally posted by GUB "Vehemently" is a bit of a strong word for it.I used the term "bickering" (as in children in a family environment) earlier in a lighthearted way.
Whether you like it or not the triangle changed at the advent of digital.
In film ISO was a measure of sensitivity
In digital it is a measure of gain.
One affects the image at the moment of image taking
One amplifies the errors of the sensor downstream from the image taking.
As for base ISO - the camera makers would tell you it is the native signal from the sensor that ISO adjustments amplify downstream. We know it aint that simple.
Film and digital are not as different as you think. Film ISO is a measure of gain in film, too. The grain size defines the gain -- it defines how big a black blot you get in the final image if the film gets hit by a few photons, cosmic ray, or heat damage. Development of a coarse-grain film amplifies the errors intrinsic to the medium (fogging) and the errors in the measurement process (Poisson shot noise) relative to that of fine-grained film.
At the level of the relationship between the brightness of the scene and the brightness of the final image, both film and digital act similarly when it comes to ISO. Higher ISO is both brighter and noisier for both types of cameras. And the reason they are so similar is that both film and digital use an amplification process (chemical amplification in film, electronic amplification in digital) to convert microscopic photons into a macroscopic effect.