(a) A firefighting vehicle is defined as any vehicle that contains firefighting apparatus and equipment which is designed and intended primarily for firefighting. The following privately owned vehicles, when operated upon a highway only in responding to, and returning from, emergency fire calls, qualify as firefighting vehicles and are exempt from registration:

(b) Privately owned vehicles or a combination of vehicles, which are not designed primarily for firefighting, including hazardous materials response vehicles, dedicated rescue vehicles, command post communications vehicles, passenger vehicles, buses, mobile kitchens, mobile sanitation facilities, and heavy equipment transport vehicles, do not qualify as firefighting vehicles as defined under subdivision (a) of this section.