The CDL laws have a class C license. If you haul haz mat or have more than 15 passengers (16 people with the driver) you need a Commercial Driver's Licenses (CDL).
If your truck is not big enough to need a class A or B license but you want to do any of the above you need a class C CDL. You would also need to add the correct endorsements to the license.
Some states use the class C as a regular drivers license. But these states also have a regular class C and a commercial class C.
My state used class D and E for non CDL licenses.
The Federal standard requires States to issue a CDL to drivers according to the following license classifications:
Class A -- Any combination of vehicles with a GCWR of 26,001 or more pounds provided the GVWR of the vehicle(s) being towed is in excess of 10,000 pounds.
Class B -- Any single vehicle with a GVWR of 26,001 or more pounds, or any such vehicle towing a vehicle not in excess of 10,000 pounds GVWR.
Class C -- Any single vehicle, or combination of vehicles, that does not meet the definition of Class A or Class B, but is either designed to transport 16 or more passengers, including the driver, or is transporting material that has been designated as hazardous under 49 U.S.C. 5103 and is required to be placarded under subpart F of 49 CFR Part 172 or is transporting any quantity of a material listed as a select agent or toxin in 42 CFR Part 73.
If you think I am still wrong than prove me wrong with a link.