What you said is true for "serious" amps....
However, very few of the small, low cost amps you're going to fine on Amazon or eBay use big-name innards like Hypex or ICEPower.
Most of these smaller ones are implemented using commercial amplifier chip-sets by a big manufacturer like TI (Texas Instruments).
And, as a VERY broad generalization, their performance characteristics are tied to that chip-set, and amplifiers that use the same chip set are somewhat comparable.
(And many of them do perform and sound very good... while some, like the Tripath amps, may have relatively poor specifications, yet still sound surprisingly good anyway.)
So, for example, there is a very popular chip-set called the Tripath 2020.
The Tripath TA-2020 is a single-chip stereo amplifier.
It delivers between 10 watts/channel and 20 watts/channel, is so efficient it hardly needs a heat sink, draws very little power while idling, and actually sounds very good.
You will find many different little stereo amplifiers on eBay or Amazon that use a single Tripath 2020 chip... and most of them deliver relatively similar performance.
(A lot of them will have "2020" somewhere in the model name.)
Even though designs using the Tripath TA-2020 are simple, there are plenty of opportunities to use fancy components, beef up parts of the design, or add features to the preamp section, which may or may not change how they sound.
You will also find different models rated differently - with two identical amplifiers using that chip set, one may be rated 10 watts/channel at 0.1% THD, while another is rated 20 watts/channel at 10% THD.
And, if you read the reviews, you will find that models by certain vendors do sound better or worse than others, or are known to be more or less reliable - so reading those reviews is a good idea.
The Tripath TA2020 and TA2024 are popular chips, as are several different Class-D chip-sets, as well as quite a few Class A/B chip-sets, from Texas Instruments and several other major vendors.
If you Google the particular chip-set used by a given amplifier you will quickly find that some have a reputation for sounding good - and others don't (Tripath TA-2024 and TA-2020 units are usually pretty good).
(If you're looking on eBay or Amazon, it's not a bad idea to search on the name of the chip set they use, so you can see a bunch of similar competing models.)
Note that, as with other amplifiers, there are chip-sets that are Class A/B and those that are Class-D.
It's worth noting that a 20 watts/channel Class A/B amp should have some nice heat sinks, or be mounted directly to a solid aluminum chassis which serves as a heat sink....
However, a typical TA-2020 chip, or a Class-D PWM chip amp, will run nice and cool with a heat sink the size of a US quarter, and a TA2024 will deliver its rated 8 watts/channel quite cheerfully with no heat sink at all .
Another thing that is important to know is that many of these small chip amps use an external wall-wart power supply - which may need to be purchased separately.
Many of them will also run from a wide range of voltages - but their performance will depend on both the voltage and current rating of the wall-wart you buy to go with them.
And, for those that come with a wall wart, you may find that some are supplied with the best option, while others are supplied with the bare minimum, and will benefit from an upgraded power source.
(Unlike with serious audio equipment, the manufacturers of cheap little amps will often give you a power supply that seriously limits performance just to save $1 or $2.)
BE VERY CAREFUL to observe the maximum ratings provided.... you really can burn out some of these by using a power supply that is a few volts over the top of their rated voltage range.
(Most provide a range of voltages they will run on. You will get more power if you choose a power supply near the top of that range - but DON'T GO OVER THE MAX RATING.)
It's also worth noting that, with many of these chip-set amps, some of the normal audiophile lore about upgrades may turn out to be totally untrue.
For example, Tripath TA-2020 amps are widely known to run very well, and sound very good, when run from a low cost regulated switch mode power supply of the sort used with monitors and surveillance cameras.
They usually run very well from a 12V 4A wall wart - and will sound good, but deliver less power, if you use a 12V 1A model.
However, "upgrading" a TA-2020 amp to a "high quality linear power supply" may actually degrade its performance significantly, so, for amps that use that chip-set, a cheap switcher is usually the BETTER option.
These little amps are a lot of fun, and many of them deliver a really nice sound for a very low price, but it makes sense to read up on them a bit...
There is a lot to know about them - and the normal guidelines for serious audio equipment don't always apply.
(And don't even imagine that you can trust the power ratings on many of them at face value...
)
Some new 'd' amps are just rebadge of either B&O or Hypex (nCore).
I think even Rotel used an ICE amp......and NAD used something off the shelf.
My PSAudio was B&O ICE and so was W4S (Wyred 4 Sound) for a long time.
I have an International Rectifier amp out in the Garage, needing a power supply.
The photo posted in this thread is interesting since it it a conventional linear PS, not a switcher.