As far as the Federal Government the FMCSA defined a commercial vehicle as follows, 49 CFR Part 390.5 a commercial vehicle IS:
Commercial motor vehicle means any self-propelled or towed motor vehicle used on a highway in interstate commerce to transport passengers or property when the vehicle—
(1) Has a gross vehicle weight rating or gross combination weight rating, or gross vehicle weight or gross combination weight, of 4,536 kg (10,001 pounds) or more, whichever is greater; or
(2) Is designed or used to transport more than 8 passengers (including the driver) for compensation; or
(3) Is designed or used to transport more than 15 passengers, including the driver, and is not used to transport passengers for compensation; or
(4) Is used in transporting material found by the Secretary of Transportation to be hazardous under 49 U.S.C. 5103 and transported in a quantity requiring placarding under regulations prescribed by the Secretary under 49 CFR, subtitle B, chapter I, subchapter C.
Notice that I highlighted INTERSTATE COMMERCE, If there is no commerce you are not considered a commercial vehicle.
Interstate Commerce is defined as follows:
Interstate commerce means trade, traffic, or transportation in the United States—
(1) Between a place in a State and a place outside of such State (including a place outside of the United States);
(2) Between two places in a State through another State or a place outside of the United States; or
(3) Between two places in a State as part of trade, traffic, or transportation originating or terminating outside the State or the United States.
So as long as the vehicle is not used in ANY TYPRE COMMERCIAL activity the vehicle is considered a private vehicle. NOW INSURANCE COMPANY USAE A DIFFERENT CRITERIA TO DEFINED AND INSURED A CMV