Difference between amps

They are notorious for misleading the consumer with their power output ratings. But that's a marketing decision.

Correct. All this stuff is. The biggest marketing decision is the one virtually all of them have agreed on, to confuse and mislead with meaningless numbers. All these numbers you're so concerned with are meaningless. Absolutely meaningless. 

What are the real or should I say physical or performance differences among these? 

Drop real, drop physical, whatever these even mean, and stick with performance. Then realize the one and only performance parameter with any meaning at all is how people say they sound. Because that is all that matters.  

It will take you a very, very long time listening to a lot of different stuff to realize this, but amplifier specs simply do not matter. Only one spec matters: speaker sensitivity. Good luck if you buy speakers with less than 92dB sensitivity. Good luck finding an amp. When you read all the problems people have matching speakers and amps first thing you should do is go look up the sensitivity of the speakers they have. Go. Look. You will see. Happens all the time. Guy just the other day took a pass on some very excellent easy to drive speakers, bought some 89dB when could have had 99dB, the ones he got will require TEN TIMES the amplifier power to play the same level.   

Good luck with that. Really superb sounding 50 watt amps are all over the place, and are actually affordable. He needs 500 watts. All because he screwed up the one thing that matter about amps, and that is speaker sensitivity. Good luck. 

So forget amplifier power. Do this one simple thing right, find speakers that sound good and are at least 92dB sensitivity you will have no problem whatsoever driving them with anything from 20 watts on up. So power ratings, forget em. Why I said they are meaningless.  

Or you can obsess with the marketing malarkey in which case, good luck! 

Other thing is, multichannel. Sorry, you want 2 channel. Stereo. Multichannel is a wasteland of crap sound quality. They suck people in with the HT BS that you need umpteen channels to watch a movie. Not true. Not even close. https://systems.audiogon.com/systems/8367 Movies on this stereo system are enthralling. Music is to die for. Posted for a reason. Study and learn.

I wouldn't know. I only buy mono amps. They are the only ones that can be installed correctly. 

Don’t forget about Jeff Rowland amps. You might be able to buy 2 used Model 12 monoblocks for a good price which might be one of your best bets. 350W into 4 ohm.

As a relative newbie, I can second MillerCarbon’s comments.  My only other comment is to make sure no matter who or what you buy, there should be a real return policy.  One week is enough enough.  Even 2 weeks is not enough.  

Everything comes down to the power supply.
You need to scale amps like they are welding machines :-)

A proper amp needs to be able to have about 300-400 watts of supply for every 100 real watts rms class A/B, 600-700 watts of class A of output, all frequencies driven.

So, in a 5 x 100 REAL watts/channel amp, 1500 - 2000 watts of power supply is needed for class A/B and 3000 - 3500 watts of supply is needed for class A. Since that is one HUGE COLLOSAL supply, it is very difficult to have a multichannel amp having the full dynamic range over every channel. Look at the power supplies that come with Pass Labs amplifiers and you will know what I am talking about. And remember that those are only for 2 channels. Imagine what they would be like for 5 or 7 channels.

Otherwise, there are not that many differences between them. Amplifier design is pretty well established & known. The rest is dependent on the quality/longevity of the components used.