The ONLY difference between the two drinks is the splash of cranberry juice which a Cosmopolitan requires. I do notknow what the intended meaning of "constant difference" is, but for a shoddy bartending quiz created by a chick who neither knows nor bothered to research the correct spelling of Kamikaze, I would not worry about having gotten this answer wrong. -LOL
The only trick answer here that might confuse you is the glass type however, both a cosmo and a kamakazi can be served as both a shot or a cocktail so the real constant difference is the lime juice in the ingredient.