The Yamahas are almost pure power amps with only a tiny bit of processing so the figure represent more closely a power amp only.
The Onkyo NR809 is not and has a ton of other features that consume power.
Now viewing the NR809 manual it states a 'no sound' draw of 95W (US), this figure then accounts for all the DSPs, codecs, video processing, AM/FM radios, switching, display, controller etc plus any supply losses at that level, ie everything but the power amps beyond their quiescent currents. How much this equipment varies in draw between idle and full utilisation, I can only guess, but it would be a fair bit for the DSPs and video processing
So, 7 channels of class AB amplifier producing 135W. Each will be about 55% efficient, so each will consume 245W for rated power. At 1/8 we have 7 x 30.6 = 214W plus additional losses through the power supply because of the higher load. If Onkyo chose, or are forced by newer regulation to use 1/3 power then the power amp contribution becomes 572W. Add that to the 95W idle, plus extras from the processing and higher supply losses and you aren't far from the 825W (7.5A x 110V) Onkyo claim. It works out even closer for the 240V models so it might be due to different measurement processes as required by law.
Best still, why don't you email them and see if they'll give a technical answer as to how they come to their figures?
I use 1/8th rated as it represents hard, but reasonable use with program material (see second pdf I linked earlier). It was also the basis for an FTC regulation back in the power wars era, but I can't be stuffed searching my paper files to find it.