There you go again, ad hominem attack. Maybe you should explain the reasons why your 800 ISO shot has less noise, instead of attacking those you don't agree with.
Think back to film days. If the subject seemed to call for more light hitting the film we had three alternatives. When possible and feasible, we could perhaps literally add more light, as in a studio situation or something of the sort, where adding light and balancing the colour with filters was one alternative perhaps. Of course the next approach would a combination of aperture and or shutter speed adjustments. The final approach was to use a higher ISO film, manufactured to be more
sensitive to light. The way I understand it, sensitivity to light is the most obvious reason for increasing the ISO, whether for film or for a digital camera sensor. Of course the downside of using a higher ISO film was the grain factor, which was eventually overcome somewhat in some of the colour and B&W emulsions. In the digital photography world, what we used to call "grain" is now referred to as "noise", or the S/N Ratio. Now after all of this rambling I believe the phrase I used previously (sensitive to light) tells the tale as far as the apparent reduction of "noise" as we increase the ISO setting. Even though the intensity of the light source does not change and nor does the shutter speed or aperture, as the ISO is increased the sensor's sensitivity to light increases, thus the reduction of noise, especially in the shadows and other darker areas of the image. Again, as you at least approach the "Optimum Exposure Level" you will start to detect less noise in those areas normally most affected by a lack of exposure.
I imagine Andrew might jump in and perhaps deflate my theory to some extent at least. However, it's the way I see the situation and understand what's actually happening when I raise the ISO setting. It does not increase the amount of light striking the sensor. The sensor is then set to gobble up more of it, and for the most part that's a good thing. I'm also certain that Andrew would offer a much more understandable way of putting it, which I look forward to.
Gary