The .223 and 5.56 are by far the most common uppers for stock AR-style carbines. After that, you’ll see .22 and 7.62s.Meh. There's really only 2 calibers widely used in the armalite platform, 5.56 and 7.62 so I wouldn't say "many different" unless you're willing to modify it. Yeah, you can make a 338 lapua mag into something that resembles armalite, but nobody does it and nobody refers to that as an AR.
I'm just saying that the ruger ar556 isn't exactly the same beast as a mini 14 so I don't like the term being used here. It's like saying that a rem .223 is an AR just because it fires the same caliber bullet as the AR-15.
As for the rest, the differences between the Ruger SR-556 and the Mini 14 Ranch rifle in terms of ability to fire rounds at short range are minimal. Both are 5.56 chambered, both capable of carrying 30 round magazines, both fire one round per trigger pull. The mini 14 tactical even has rails to put the same kind of attachments that you can on the AR model. The main difference for most is that the mini 14 looks like an old wooden rifle while the AR looks like a military rifle.
You can buy uppers for AR-15s on almost any caliber and almost any idiot can make the modification. But none of that matters in reality when all of them are still limited to one round per trigger pull.