Sorry, in short you're wrong, yes they do. I'm on my phone so I will be brief. The ISO determines the sensitivity of the sensor in the camera to the photons h

Sorry, in short you're wrong, yes they do. I'm on my phone so I will be brief. The ISO determines the sensitivity of the sensor in the camera to the photons hitting each bucket in the "sensor array". This sensitivity combined with frequency of the photon hits determines the data that makes up the actual image. If you could theoretically dump the RAW data from an image recorded for a different ISO for the same image, it would be different for each one. You can't "boost" an image's ISO post-capture, because the sensor data is already captured. What you can do is increase the values of those pixels that are appreciably close to buy not equal to zero, but for which data exists, giving the impression of pulling out data from the shadows, but the limitations/complexities are too much to go into here. When you do so in practice, you do not have as much relative detail in those extremes. What we interpret as "noise", typically in high ISO low light photography, is a real thing that the computer cannot perfectly compensate for, because it's a fundamental property of both the hardware, but more importantly, of background light/radiation and the probability/quantum nature of light...