After pounding info into my head over the last month, I think this is coming clearer now. Let's see if I have this straight...
AMD63 is not the same/is not a misunderstood iteration of AK63D. They are distinct and different rifles, separated in time of manufacture by the AMD65.

So, first came the AMD63, then the AMD65, then the AK63D. Correct?
But they are ALL AKM with regard to barrel diameters and measurements, correct?
So when I am shopping for a barrel for my AK63D kit, I should be looking for a barrel that the seller says fits an AMMS or AK63D or AKM, correct?

So, something like this???: http://ak-builder.com/index.php?dispatch=products.view&product_id=29781

Also, for those who have done it, does this: http://ak-builder.com/index.php?dispatch=products.view&product_id=30146
Plus one of these: https://www.cheaperthandirt.com/product/tapco-m16-style-ak-47-muzzle-brake-762x39mm-14x1-left-hand-thread-steel-manganese-phosphate-finish-ak0685-751348005898.do?sortby=ourPicks&refType=&from=fn

Equal 16 inches?

Thanks in advance for any replies!!!

If you use the shorter barrel you will need to use on of these longer muzzle brakes & permanently attach it by welding or blind pinning it to be legal. Or you will need to SBR it.
http://ak-builder.com/index.php?dispatch=products.view&product_id=30042

Then I would just get a 16" barrel. It looked like it would work, and then I did the math. 14.375" for the barrel + 1.75" for the A2 = 16.125", but you gotta figure there is more than 1/8th of an inch of threads being used that needs to be subtracted from the A2 length.

Any recommendations on the type of barrel I am looking for? What I am really trying to say is, If I input into Google: "Hungarian Underfolder barrel for sale" or "AMMS Barrel for sale" or "AK63D barrel for sale" I don't get what I am looking for, just a bunch of parts kits with barrels included. I mean, this chart sites specs on Hungarian "AKM-style" rifles.... but WHICH Hungarian rifles are AKM? AMD63? AMD65? Ak63d? All of them?

There really isn't any AMD63. Just an AMD65.

AKM63 now we are talking and there are many variants to it with their own designation but one of them wasn't the short barrel, they were all normal length AKM barrels.

Do you mean to type AK63D? Because that is the kit I am researching.

It is very confusing. In this wiki page on the AMD65 - https://en.wikipedia.org/wiki/AMD-65

The following quote says:

(Bold added by me)

I now realize after reading that yet a fourth time that I erroneously wrote AMD63 in the OP instead of what I meant: AKM63
regardless, what THIS wiki implies is a manufacturing order of AKM63, then AMD65, then AK63D

But.. the upshot of what you are saying is (correct me if I'm wrong), the Hungarian underfolder that is for sale in various places called the AK63D will require a typical AKM barrel like I linked to at AK builders here:
http://ak-builder.com/index.php?dispatch=products.view&product_id=29781