Merriam-Webster's first definition for box is 'a rigid typically rectangular container with or without a cover', but 'box' is also commonly used for 'cardboard box', which is probably what you are packing the samples in.
The reason we ever felt compelled to say 'cardboard' before 'box' is that the word actually derives from the box tree, suggesting that boxes are made of wood.
box (n.) Old English box "a wooden container," also the name of a type of shrub, from Late Latin buxis, from Greek pyxis "boxwood box," from pyxos "box tree," which is of uncertain origin.
Carton, on the other hand, derives from a word meaning 'paper':
carton (n.) 1816, from French carton "pasteboard" (17c.), from Italian cartone "pasteboard," augmentative of Medieval Latin carta "paper" (see card (n.)). Originally the material for making paper boxes; extended 1906 to the boxes themselves. As a verb, from 1921.
Dictionary.com defines 'carton' as 'a cardboard or plastic box used typically for storage or shipping'.
So a 'carton' is a type of 'box', but as your own research has shown you, boxes can be made of harder materials than those typically used to make cartons. I wouldn't insist that you use one word or the other, but sometimes the slight difference in their meanings can be useful.
In shipping large quantities of packaged items (smaller boxes) within one large box, you might choose to differentiate between the contents and the container by saying that you are packing a number of cartons (less durable boxes) into a box (suitable for shipping).