AS you have heard, American "cookies" are usually crisp, but others are chewy ("soft").

I don't know how long the "soft" kind have been common. I first noticed them ca1960. I thought they were something new and strange, and it took me a while to get used to them.

(Fig Newtons, of course, have always been chewy, but although universally considered "cookies," they're closer in nature to tiny pastries.)

Sweetness is the common denominator. An unsweet (or slightly sweetened) crisp "cookie" is a "cracker." An unsweet fluffy thing is either an "English muffin" (a kind of bread) or a "biscuit" (a kind of bread raised with baking powder or baking soda). "Scones" are uncommon, though growing in popularity; people generally unfamiliar with them think of scones as a kind of "biscuit."