A "carton" is specific. The word makes me think of a box that is made of corrugated cardboard or some similar material. It often means a sealed package of something to be shipped or sold. A "box" is general. It means any container that is more or less squared-off in shape. A bank "safe deposit box" is made of metal. We keep some things in a plastic storage box under our bed. "Box" can be even more general than that. It can mean a square or rectangle to be filled with a mark or writing; a "checkbox," "type 'italki' into the search box." It can mean a compartment that isn't really very square at all. It can mean a box-shaped object full of electronics gear, a "boom box," or the "black box" in a car that records data.

There is a difference between UK English and American English with this word. in the Uk we only use the word carton for the "carton of milk" we buy in the shops. Im not aware of any other use. In the USA a carton can be any box which is light in weight and not made of, or carrying any heavy materials.