What is a commercial motor vehicle?

depends on how you register the vehicle. A truck could be registered as passenger vehicle for private use and not carry a payload

IN ADDITION:

Generically speaking, a commercial vehicle is one used in the furtherance or support of a business endeavor.

Any such vehicle used to transport property which has a Gross Vehicle Weight Rating (maximum safe loaded weight per the manufacturer) of 10,001 lbs. or more, or which is designed or used to transport more than 8 persons (driver included) for compensation, or more than 15 (driver included) without compensation or is used to transport hazardous materials in quantities sufficient to require placarding is subject to state and federal regulations for CMVs.

The definition for commercial driver's license regulations does not apply to vehicles with a GVWR under 26,001 lbs. unless transporting certain quantities of hazardous materials, certain toxins or is designed or used to transport 16 or more people.