Sorry, but are we talking about the same thing? The variable specs are usually stated for output power which depends on the load and whether RMS or peak. The stated consumption power rating should be about the same whether testing at 4 ohm or 8 ohm loads, etc. so they only give one value.
We are talking about the power consumption spec given in manufacturers specs on websites, owner's manuals or datasheets. Take a look of some examples:
Yamaha RX-A3080:
Power Consumption........................................................................ 490 W wt. 39.9 lbs, rated output 150 W, 8 Ohms They also provide a "maximum power consumption" but again, without stating the test conditions.
Denon AVR-X2600H:
Power consumption:......................................................................... 500 W wt. 21 lbs, rated output 95 W, 8 Ohms
For power amp, again let's look at Yamaha's 11 channel MX-A5200:
• Power Consumption ....................................................................... 650 W wt. 58.2 lbs, rated 150 W, 8 Ohms
• Maximum Power Consumption (All Channel driven, 10% THD)... 1,500 W
So you can see that THD also affect the number, as expected.
This is just one comparison example, to show those numbers likely don't represent the power consumption when the amp is driven to its "maximum power levels".
And no, if the power consumption spec is what you think it is (which could be true in some cases but we really don't know), then the numbers will not be the same whether testing at 4 Ohm or 8 Ohm load, that is just not possible based on basic electrical theories. It will also be further complicated by the fact that it would depend on the duration of the test. For example, if it is a 1 minute test, the output will very likely be higher than if it is for 30 minutes (for AVRs anyway) so the consumption will also be higher during that 1 minute test.
This spec is just not very meaningful, it is of course meaningful and useful to a point. For the average consumers they may be misled, or confused no doubt about it. Just do a search even just on this forum and you will see how often people even assumed the power consumption specs = the amp's actual maximum output. For example, I have seen more than once, someone opined that there is no way a mid range Denon AVR can output 100 WPC, 5 channel driven because the power consumption is only 660 W, because class AB amp's efficiency is only 50-60% etc., blablabla...
When you see such claims or questions, you will know people in fact were confused, or misled.
The moral of the power consumption spec story is, take it with a grain of salt, it could mean differently depending on brands, models, conditions of test, use etc., that are not specified more often than not.