I'm still amazed that so many people who clearly know very little about this fight so hard to persist in this faulty 'amplification' metaphor.
Here's the simplified view I like to use, since a picture is worth a thousand words:
Depending on the camera's implementation, ISO setting can trigger any one path; or any combination of those paths.
ISO does not describe anything to do with the path--only the output at predefined input & output values (or difference between input & output).
So...
- Will ISO change amplification? Potentially.
- Will ISO alter processing? Potentially.
- Will ISO simply digitally scale? Potentially.
- Will ISO change amplification, processing, and scaling, together, all at once?
Potentially.
And...
- Can you say that ISO always changes amplification? No.
- Can you say that ISO always changes processing? No.
- Can you say that ISO always changes digital scaling? No.
Most cameras automatically attempt to optimize the path for a middle grey output in a pre-defined JPEG rendering style. The results are relevant to ISO. How it get the results is irrelevant to ISO.
In other words, this entire conversation trying to generically link ISO to amplification is a pointless exercise because there is no universal correlation.
So finally...
- Can you get the same results changing ISO setting vs processing & scaling?
Depends.
- Can you make a universal rule?
No.
- What should you call this difference between input & output?
I don't know. Amplification? Scaling? Neither is technically accurate.
Maybe "pushed." Or "rendered." I personally don't care as long as it makes sense in context.
Or maybe we go with just "ISO" and stop trying to come up with imprecise synonyms that may not exist. 
Even though ISO is not measured by manufacturers against raw, it is recorded with the raw (even if it's just a tag for digital scaling). So let's keep things simple.
"Here's a raw image. I exposed at 1/250 and F/4 on a full frame. ISO 800."
What does that mean? Different things on different cameras. So cross reference that information with the camera & any camera-specific data points to sort out what that means if you want. Let's not try to define universal terms that won't exist.
When you set an ISO, you're effectively telling the camera "This is my expected level of output brightness. Please optimize middle grey in this image for me."
When you lower the ISO, you're telling the camera "I want to optimize for highlights."
When you raise the ISO, you're telling the camera "I want to optimize for shadows."
Bobn2: thread limit reached, but I think you meant "precision" (ie. scaling) not "accuracy" in your multimeter analogy
here . That's primarily how I use mine.
"Process" is an umbrella term which can be further reduced, and there is no cleaner way I can immediately think of to illustrate the process. For example, software requires hardware. Each step could involve scaling, but not every step involves digital scaling, etc. And that's why it's explicitly a "simplified" view that shows that there is no 1:1 with the semantics being used.
