The AR-10 was originally made as a 7.62x51 battle rifle in the 50s by Eugene Stoner when he worked for the Armalite division of Fairchild. A few years after he developed the AR-10, he scaled it down for the .223 Remington cartridge and called it the AR-15. Colt bought the rights to the AR-15 and AR-10 in 1959 and successfully campaigned the AR-15 to replace the M-14 as the US Army issue rifle as the M-16.
Just as Colt owns the trademark to the AR-15 name, Armalite (now owned by Strategic Armory Corps) owns the trademark for AR-10. Some folks get pissy when you refer to non-Armalite, large-frame gas guns as AR-10s. Same folks should get equally pissy about calling small-frame gas guns AR-15s.
As said above, an AR-15 "style" rifle is
normally built to interchange parts with any other mil-spec M-16/M-4 style rifle or carbine. As such, the magazine well is only large enough for the standard 5.56/.223 magazine. I've never had a 300BO or 6.5Grendel upper, but now that I have a 9mm AR "pistol" with an Octane 9 silencer, I may just have to build a 300 upper to play with. Probably end up Form 1 on the 9mm lower and one of my 223 lowers. Some folks call these AR9s.
Since the AR-10 was never adopted as a US standard battle rifle, and the MK11/M110 are the only military rifles adopted on any scale by US military, there have been numerous paths taken by different designers to produce an AR-10 "style" rifle without violating patents, which have now expired, or making their own improvements to aid reliability. This leads to non-interchangeable parts like bolts, firing pins, bolt carriers, barrel extensions, magazines, etc. In general, all have shifted away from the hooked charging handle under the carry-handle/rear sight base in favor of an extended version of the M-16/AR-15 version. Some parts are interchangeable. Most accept AR-15 pistol grips, most accept large-frame charging handles, most accept AR-15 triggers and receiver extensions (buffer tubes. Due to the longer bolt carrier, though and the need for a longer stroke, an AR-10 rifle-length buffer is shorter (by 1 weight) that an AR-15s rifle length buffer. Some who build their own large frame ARs find this little issue out the hard way when their rifle doesn't reliably catch the bolt catch or will not reliably pick up another round from the magazine.
At one point, I owned an Armalite AR-10, built from a receiver set with a 20" Wilson barrel in 308. It was a hammer and I liked the handguard enough to get one for my 223 carbine. Uses Armalite magazines
only, and they weren't easy to get. Now Armalite has them in stock for $35 each. Figures.
Ended up selling it to build a Mega Maten in 6.5cm. Wanted some longer legs and ended up getting a 308 upper off the PX to go with it. This takes KAC, ASC, Magpul, DPMS magazines. The only ones that didn't work reliably for me were the DPMS.