Does unperfumed, or unfragranced mean there is no perfume in the product?
No, unfortunately it doesn’t. These terms usually mean it is a version of a product, say a deodorant, that has not had a scent added, like other versions in the range, which will be called shower fresh, or country garden or something to give an indication of at they are supposed to smell like, and some of them really do! However, the chemical bases of some of these products smell so disgusting that at the base stage, they mix in perfumes to overcome the awful smell of the product. What they then have is a fairly neutral base product which doesn’t really smell of very much, but has not had any country fresh added yet. So unperfumed can mean it has had perfume added, but has not been given a distinctive perfume smell.