A snow blower is a product; not dying from the cold is a need; having the newest most expensive snow blower to reduce effort and impress your neighbors is a want.
A restaurant is a service; nutrients is a need; having a pizza in a cone so you have something to tell your friends is a want.
Football is a product; cardiovascular health is a need; $300 new edition shoes to stand out is a want.
The product or service really has nothing to do with anything.
People may place it in these categories but they always relate to them in needs and wants.