Corrugated boxes are manufactured in single, double, and triple “walls” (see above picture). Most items can be packed in a single-wall box, but if an item is very heavy or bulky, a heavier duty box is recommended. Tri-wall boxes are very large boxes generally used for transporting oversized, heavy items or a collection of boxes/suitcases/duffle bags.
Packing fragile items brings on a new set of requirements. For example, if you were packing a crystal bowl or several dishes in a box, you could use a single-wall box with plenty of bubble roll around each dish. But, if you were packing an entire set of dishes/china in one box, you would definitely want to use a double-wall carton (such as a “dishpack” or “china barrel”), and of course, plenty of bubble roll.
Be aware that if you are shipping an item in its product box (for example, a kitchen blender or a set of pans), the product box is not a suitable shipping box, even if you repack the item in the same packaging it came in. For shipping, it should be repacked with bubble roll and fitted into a slightly larger box meant for shipping. Those product boxes are very thin and have no protection again the rigors of truck transport and conveyor belts.
For an excellent description of all the different standard moving boxes, click here.
Remember that shipping rates are determined by the weight and dimensions of a carton. The larger the carton, in general, the higher the cost to ship, even if it only weighs a few pounds.