The primary difference is the caliber.
The AR-10 is a .308Win./7.62NATO
The AR-15 is a .223Rem./5.56NATO
*Beware of SOME surplus military ammo*
For the most part they are identical except the really early AR-10's, they didn't have the now common style charging handle. They had a charging mechanism which looks like an upside down trigger located within the carrying handle.