There's a difference between a "Commercial Motor Vehicle" and a "Commercial Vehicle". They are easily confused because common sense would tell you they are the same. But the DOT is not one to have common sense. A "Commercial Motor Vehicle" has special meaning for the regulation of heavy and dangerous vehicles, as Moot shows with the DOT's regs. Heavy or HAZMAT, or carrying enough passengers and you're a "Commercial Motor Vehicle". The DOT and the FMCSA is all about the safety of the public and the environment.
Not all "Commercial Vehicles" are "Commercial Motor Vehicles", but all "Commercial Motor Vehicles" are "Commercial Vehicles".
A "Commercial Vehicle", with few exceptions, has a meaning that is dealt with at the state and local level, generally starting with license plates. Generally speaking, any vehicle used in commerce, is a "Commercial Vehicle". A cargo van with no lettering whatsoever, but with commercial plates, needs to stay off the Natchez Trace and the other places where it says "No Commercial Vehicles". A plumber's van, a floral delivery van, a pickup truck with commercial plates because the owner had the vehicle registered to his business, these are all "Commercial Vehicles". Any vehicle with commercial plates, or even one with non-commercial plates but has the lettering of a business ("Bubba's Audio and Annoying Anti-Theft Alarms" on a Camry) are considered "Commercial Vehicles" in most localities.