Do I have this right? Multi cal would mean 5.56, .223. .22lr, .300ac.

But NOT 7.62 NATO or .308?

And as far as the lower is concerned, is .308 and 7.62 NATO the same?

You would need an AR10 receiver for those rounds.

.308 is commercial ammo, 7.62 NATO (aka 7.62 x 51) is the international military designation. Just like .223 & 5.56, the military variant is loaded hotter and has a hard primer to prevent slam fire.

I was pretty sure I'd read differently, and a quick Googling turned up this page: http://www.303british.com/id36.html

From what it's saying, the 7.62x51mm brass is thicker than .308, the chamber is typically a bit larger, and the .308 is actually loaded to slightly higher pressures:
'Commercial ammunition has a SAAMI/ANSI maximum pressure of 62,000PSI. '
'Military ammunition is loaded to maximum average pressure 50,000 CUP (approximately 58,000 PSI using the modern piezo transducer method of measurement). '

I know that's not the only place I've seen it, but I'm certainly no expert.

Ok, then I immediately found another page that said the pressure wasn't the issue but that it was the headspace: http://how-i-did-it.org/762vs308/chamber.html

'Safe chamber headspace for the .308 Winchester cartidge is between 1.6300 and 1.6340 inches. The equivalent minimum and maximum values for 7.62x51mm NATO chambers are 1.6355 and 1.6405 inches.'