AR-10's are essentially chambered for 308 Win (7.62x51 NATO), but since there are many different calibers made off of the 308 case, it can accomidate those chambers for the most part: 7mm-09, 260 Rem... Essentially the same case, but different neck sizes.

The AR-15 has the same thing going on as the AR-10's but it's more to do with the size of the head of the case. If the head of the case will fit in the bolt and work in the mag, it will run in the gun if the barrel is changed: most common are 6.8 SPC, 6.5 Grendel, and 50 Bewulf.

Some parts are interchangable, but most are not. The biggest visual indicator between the two is the magwell. The AR-10 is cut much higher in the front to accomidate the larger magazine. Most AR-10's have a different charging handle or mechanism than an AR-15 too.

Don't get too wrapped up about it. It takes time.