Candy is pretty close to the British "sweets", near as I can tell.
We have a British sweet shop in the mall (yes, its called a sweet shop), and everything in there is something I would consider candy. Gummies, Smarties, peppermints, taffy, licorice, all of that is candy.
Non-candy high-sugar stuff is usually more along the lines of baked goods (cookies, cakes, rolls, etc.), or drinks.
Fudge, for example... is a grey area. If it comes in a candy-wrapper, its candy. If its home-made, its not. (really confusing, right?)