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Same lower and upper receivers, different barrel and BCG.
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+1, except the carriers are identical, too - just the bolt and the barrel which are different.
As mentioned, Colt used to just provide a standard 5.56 magazine with their 7.62x39 Sporters, but you quickly learned you couldn't load them full and expect them to feed properly. The magazines also hold fewer rounds than their rated 5.56 capacity when loaded with the larger-diameter 7.62x39 cartridges.
I've never had a 7.62x39 AR but do currently have a 5.45x39 AR. It has some of the same problems with regular AR magazines and feeding. I've used C-Products 5.45x39 magazines with it, though, and those seem to feed just fine. Maybe there are similar dedicated 7.62x39 AR magazines available.
There were, and may still be, "franken-mags" which were the straight portion of a 5.56 magazine joined to the strongly curved body of an AK 7.62x39 30rd magazine, and those reportedly worked pretty well.