I don't know for sure but I believe the term Class III is given to dealers who may transfer fully automatic firearms and destrictive devices through their business and purchase them from the original manufacturer. Title II, how it has been explained to me, is the classification given to fully automatic firearms and destructive devices that mandate the purchaser to obtain a National Firearms Act stamp that is approximately $200, an ATF or FBI background check, and local Law Enforcement endorsement. Title II devices are purchased from Class III dealers. In other words, if I understand it correctly, you do not have to have a Class III to own a full auto, but you do to sell them in your FFL store/business or to purchase them directly from the weapon's/device's manufacturer.
If any of the above is incorrect, please educate me guys.