most current AR chambers are .223 / 5.56 WYLDE chamber meaning both will fit and function.
the problem comes from a straight up old school .223 being fed 5.56.
the evolved gas pressure is higher for the 5.56 round, and will probably work for a while, will put extreme use on the rifle and will eventually malfunction probably with similar results to the .300BLK problem.
a 5.56 can be forced to chamber in a 7.62 chamber, but is about 6mm too long so you will know theres a problem
7.62 nato of standard configuration wont fit the lede [ogive] of the 5.56 chamber unless you shove really hard with a mallet.
what you may see is a lower receiver stamped for 5.56 NATO assambled with a 7.62 upper and barrel. this is proably fine for most aluminum lowers but i would stay clear of the polymer lowers or the skeletonized milled out lowers, for the 7.62
the last paragraph is not exactly correct, a lower receiver for 556 NATO STANAG magazines has a different length magazine well (AR-15 derived design, not AR-10) and cannot take the dimensions of an AR10 magazine/7.62 NATO magazine.
you can mistakenly chamber a .300 blackout in a 556 nato rifle upper because the blackout is the same length cartridge as a 556 nato round and will feed.
you cannot mistakenly shove a 7.62x51 NATO/.308 winchester round into a rifle lower/upper that is not an AR-10 derived design because there would be no way to even seat the magazine.
even if you were to somehow mistakenly mount an ar10/762 NATO upper and barrel on an ar15 lower the only way you could try to get a round into the chamber would be to shove it in sideways through the ejection port
>>what you may see is a lower receiver stamped for 5.56 NATO assambled with a 7.62 upper and barrel<<
5.56 magazine wells can be modified to fit 7.62 magazine there a couple examples on the range right now, also a .375 win magnum necked down to a .223 projectile.
up here its common to ammo up with a full mag, +1 one in through the out door
if you have a photo example of someone actually doing that on an ar15 magazine well i'd be very interested to see what the hack job looks like
why would someone actually chop a lower? because its not available, or its a do something winter project to chase off the cabin fever.