Bill - all digital cameras capture at their own 'base ISO'. Most cameras this is ISO-100, some might be higher, such as ISO-125, some all the way to ISO-200. The image is then amplified (or downgraded) to the ISO specified by the exposure setting, either the human or the camera's calculation. The numbers below the base ISO are just more trickery of digital photography, not the 'base ISO' of the camera. How each camera does this is proprietary. The only issue is the result maps to the ISO international standard -- International Organization for Standardization, a nongovernmental organization that publishes standards.

So, the base ISO is the unamplified sensitivity of your camera’s sensor. Your reference to the lower values, below ISO-100 are not the base, unless confirmed by the manufacturer. ISO-080, 60, 50 are 'expanded' values. These expanded values reduce the dynamic range capability of the camera, just a values higher than the camera's normal range, such as higher than ISO-3200, check your individual user manual. When you use a lower ISO setting than your base (i.e. ISO 50 instead of ISO 100) such as to achieve a slower shutter speed, your camera sensor will digitally expose your image at ISO 100, and then the processor will reduce that exposure to simulate what it would look like at ISO-050.

The result? You can potentially lose contrast and detail in the highlights and reduce your overall dynamic range since the image is purposefully overexposed. Highlights that are on the cusp of being clipped at ISO-100, when you meter the scene, will likely be blown-out from the exposure being brought down.

Recient conversations and articles about the new Sony A9iii have me wondering if I understand the meaning of ISO and spicificly "base ISO" as it relates to modern digital cameras.
First off
Iso, from film days, must have been an standardized across all film manufacturers. (?) As I understand it, ISO had to do with a films sensitivity to light which was based, I think, on the "grain size ?" of the silver halide crystals. Larger crystals captured more light and also led to the Grainess of higher iso films.

In digital photography the ISO is an amplification of the light signal captured by the sensor.
The sensor captures whatever photons it captures but the electronics in the camera amplify (gain) the signal as we turn up the ISO.
I'm sure I'm going to be seriously corrected on all of this, which is why I'm asking.
Here is where the confusion for me starts
If ISO is a carry over term from film, what exactly is a "Base ISO" of a particular camera. Spicificly,
Why does Nikon use a base ISO of 64, Canon 100, Olympus 200 and Now Sony a9ii 240? And I may be wrong about some of these Base ISOs but I hope you get my question.
To the photographer, what difference do these numbers really make?
Am I to understand that Nikon's ISO 64 is its cleanest, least distorted but also less light sensitive then say Canons ISO 100? That Olympus and now Sony are using sensors that are more sensitive (their base sensitivity), collecting more light comparatively at their respective base ISO and producing their cleanest "recording" of that collection?
Please explain.