In an AR-15, the bolt and carrier are the "action." The upper receiver serves to hold the barrel and give the bolt carrier a place to ride. There's no integral relationship between the receiver and the firing mechanism. That's different.
The bolt carrier, well, carries the bolt back and forth in the upper receiver. It functions to house the bolt, sure, and also to reset the hammer. The carrier also bears the brunt of the gas pressure during operation; this pressure moves it back to cycle the firing mechanism. The bolt carrier has nothing to do with headspace. That's all in the bolt. Using the same (checked and checked off) bolt in different carriers is accepted as "safe."
Bolt carriers come in two basic configurations and then a number of unique takes. The essential designs differ mainly at their back ends. AR-15 carriers have a small tail while the M16 carrier has more metal. The M16 carrier has a shrouded firing pin and therefore requires a "large collar" pin style. The extra collar diameter is necessary for it to be reset. When Colt did the "receiver block" to prevent owners from installing any full-auto parts, they sliced the rear carrier bottom slap off.
To the semiautomatic shooter, the differences in these carriers come down to weight. The M-16 is heavier. That's good. Now, I can't tell you to run out and buy one. M-16 parts without Class III validation are a violation of the National Firearms Act. That's federal law. There are a few "match" carriers possessing forms virtually identical to the M-16's. This, as anticipated, is done to increase carrier weight. Some also like the shrouded firing pin because they think it's more reliable. In a cleaned rifle, there's no difference. Dirty guns are unreliable, no matter which parts they're made from.
How important is bolt carrier quality? Let's say that quality is simply dimensional correctness and mil-spec metallurgy. Since carriers from reputable manufacturers are produced with proper substance and heat treat and within tolerances better than mil-spec, carrier "quality" isn't really a factor in how well anyone's rifle will shoot. There have been, and no doubt still are, bad carriers floating around. Some are foreign-made rejects, and a few domestically produced that fell off the back of the truck. These are not made to mil-spec. The heat treat or dimensional conformity aren't right. You won't get a bad one from DPMS, Bushmaster, Colt, Fulton Armory, FN or the Brownells catalog. Wink...