First of all, what is fragrance? Fragrance technically means an artificial fragrance with a long list of chemicals we cannot pronounce. The list of ingredients is so long, they are just labelled as fragrance. Pure essential oils are not considered fragrance. Although fragrance-free Bebebalm does not contain essential oils either.
Fragrance-free means there's no artificial fragrance added. The faint scent you smell is the actual scent of the ingredients.
Unscented means the scent is masked so you don't smell anything. Artificial fragrance or chemicals may have been added to hide or disguise the scent.
If you've got sensitive skin or are prone to rash, pick fragrance-free products.