Which word you use would depend on which part of the world you are from. In South Africa, for example, the word box is used for containers of all sizes big or small. A box of juice, a box of milk, a box of cereal, etc. In some countries the word carton would be used for smaller containers, such as those used for food kept in a fridge like milk or juice.

Carton a small, light box or container in which drinks or foodstuffs are packaged. "a carton of milk" and a box is storage container with a flat base and sides, typically square or rectangular and having a lid.

A carton contains liquid and a box is used for storage of units of items.