Gunsmithdude:

You are correct that the secret to accuracy and much function is in the upper receiver group, especially the carrier group and barrel extension.

The lower receiver group is a bigger influence for reliable feeding and powering the return of the carrier groupe.

Simon is correct that AR-10 is a registered ArmaLite trademark.  It is not correct that it is a generic term.  It has been established, announced, and protected in four cases of other companies attempting to use part of the trademark.  Private users will sometimes misuse the term, but ArmaLite is required to strongly defend it, and will continue to do so.

"AR stands for ArmaLite"

Quoted: You are correct that the secret to accuracy and much function is in the upper receiver group, especially the carrier group and barrel extension.

More specifically, the accuracy comes from the fit of the ammo to the barrel, so you want a perfectly centered throat that's very close to the diameter of the bullet.
You want this chamber in a good quality barrel blank with a good crown on it.
Now you want this barrel in a free floating handguard so that gun handling does not influence point of impact.
Lastly, you want a good trigger in the lower so you have good control of when you let a  round loose.
Everything else is fluff.
Armalite makes good stuff, get the AR-10T and you will have a good barrel, handguard and trigger as well.
If you don't like the barrel options that the factories offer, I can make you anything you want and it will be accurate.