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.