No. Fragrance in products is usually made of mineral oils or synthetic chemicals. So, when a product claims to be fragrance-free, it basically means that the formula does not contain those chemicals that make fragrance. But that does not mean the product will not smell. It will still have a smell of its ingredients.
Unscented means that the product has no smell whatsoever. But, to achieve this ‘no smell’ status, the product has to be loaded with chemicals that will neutralize or eliminate the natural smell of the ingredients.