There are eight different classes of commercial motor vehicles in the USA, and they are divided into three more generalized categories. Light Duty, Medium Duty, and Heavy Duty.
These trucks can be classified by their GVWR (Gross Vehicle Weight Rating).

Light Duty Trucks
(Classes 1, 2, and 3)
Class 1: GVWR: 0-6,000lbs
Class 2: GVWR: 6,001-10,000lbs
Class 3: GVWR: 10,001-14,000lbs

Medium Duty Trucks
(Classes 4, 5, and 6)
Class 4: GVWR: 14,001-16,000lbs
Class 5: GVWR: 16,001-19,500lbs
Class 6: GVWR: 19,501-26,000lbs

Heavy Duty Trucks
(Classes 7 and 8)
Class 7: GVWR: 26,001-33,000lbs
Class8: GVWR: Greater than 33,001lbs

A CDL (Commercial Drivers License) is required by drivers who operate certain heavy duty vehicles. An individual who possesses a Class A CDL can drive any size heavy duty truck. Class B and C CDL's are more limited in what type of heavy duty truck an individual can operate. (Mainly with restrictions to trailer/passenger capacity)

See the image below for a breakdown of vehicles and their classes.
Truck Classes.svg