I'm sure babirl will jump in here to correct me if I'm wrong on anything, but I'll outline the basics.

SPC was the original chamber that was approved, also commonly referred to as the SAAMI I chamber. DO NOT buy a SPC I or SAAMI I barrel. Also, most of these barrels have a 1/10 twist rate. This is not fast enough, and many bullets will not properly stabilize. Although less common, these barrels are still out there, so beware.

The specs that got approved initially were not optimal, so the SPC II was developed to correct the problems of the original SPC chamber, primarily a longer leade and better angle at the front of the chamber (I forget what this is called). SPC II barrels typically have a 1/11 or 1/11.25 twist rate. SPC II barrels can handle any factory ammo, including Silver State Armory's "Combat loads" or "Tactical loads" SPC II barrels and chambers are fairly common now.

The 6.8 DMR, DMR-C, and ARP chamber are all very similar. They either have tighter or looser tolerances, but can fire any 6.8x43mm ammo safely. These were all developed by Harrison at AR Performance down in Pueblo to increase accuracy and performance. He is literally one of the pioneers of fixing the 6.8 chamber. He also corrected the twist rate and determined that 5R rifling is the way to go.

6.8x43mm refers to the cartridge dimensions. If someone says 6.8x43 ammo (as I usually do) they are probably referring to updated and possibly more powerful ammo that should not be used in a SPC I or SAAMI I chamber. Only use this ammo in a SPC II, DMR, DMR-C, or ARP chamber. For best performance, use this ammo in a barrel with a 1/11 or 1/11.25 twist rate. Last I heard, the 6.8 community was trying to push the use of "6.8x43mm" to denote an updated chamber and to get away from the whole "SPC" moniker.

If you have more questions about 6.8 stuff, keep asking!