You ask for “another word to explain the material which is around the package itself” and for unique words for, apparently, multiple boxes or cartons stacked on pallets vs a single empty box, carton, case, or crate. I don't understand the question's aim or if you want the name of a material, or a term referring to the material, or a term that means pile of boxes, or an empty box, and probably it's something else entirely, but c'est la vie.
For the material itself, it seems reasonable to refer to cardboard, corrugated or not.
For a term referring to the material a box is made of, consider casing material or wrapping (“The material in which something is wrapped”).
As a generic term for enclosures or packages that focuses on the package shell, consider encasement (“something that encases”), or casing (“That which encloses or encases”), or wrapper, or perhaps box-type.