The distinction made by Liz has no meaning in America, where cookies, depending on moisture content (and molasses or other content in some) may be soft when they are bought or made but go hard as they dry out. Most are hard when fresh and stay about the same for the few days they remain uneaten.
'Biscuit' seems limited in usage to certain products in England; the American 'cookie' covers a much broader range of product. One of the few store-bought cookies I like is a molasses-ginger cookie, soft when the bag is opened, but hardens with time. Going soft is usually associated with high humidity and mold, and quick disposal in the trash.
Of course much of America has low humidity and almost everything quickly goes hard and dry if exposed.

'Biscuit' in America applies only to the quick soft breads, 2-3 inches in size, baked in the oven or on stove top and served hot with butter, gravy, molasses, jams or jellies, etc.