There is no difference in how class D amps are rated compared with class AB amps.
The problem is that different manufacturers have in fact rated their amps using different metrics (such as "peak" versus "RMS)", or "burst (20mSec versus continuous (or continuous for amplifier purposes). For bass guitar or guitar purposes, THD is nowhere near as important as for other applications because the instruments themselves generate 10X the THD the amp does under linear operation.
You have to use your brain a little bit to sort through the specs, some manufacturers provide comprehensive specs that clearly state how the power is measured and some manufacturers provide almost no information (or information written by the marketing department without control of the engineering folks). I am strongly in the first camp as a designer.
Regarding power input versus power output, what you may be missing is what the safety and EMC regulators require for how power input is calculated. I have done these calculations here many times yet it still seems to be misunderstood.
Let's say an amp is rated for 1000 watts RMS into 4 ohms. The regulators require that the AC power (or current) draw is printed on the back of the amp and it's based on 1/8 of rated audio power, though it can be more IF the amp is designed and intended to be operated at higher than 12.5% duty cycle. 1/8 of 1000 watts is 125 watts (which is 1/8 of rated audio power). Now, the amp and PSU efficiencies must be factored in, a typical class d amp with SMPS is going to be about 85% efficient so the input power is 125/.85 = 147 watts. This is how the power draw number is arrived at. For a typical class AB amp w/ line frequency power supply, the efficiency number is going to be around 50%, so the power draw would be 125/.5 = 250 watts.
Different designers qualify their amps differently. For example, I have (very) detailed specifications for my products, and they are easily understood by professional engineers who design and test amplifier products. They would look like Greek to an average person however. Like the amps themselves, different designers place different levels of importance on different aspects of their products. As a word of caution, I have seen significant mistakes made by magazines that have attempted to measure things that they did not fully understand. This causes folks who don't understand this to draw incorrect conclusions which get perpetuated like a bad rumor.