A "strong box" or safe, is a secure lockable box for storing money or other valuable items. The term "strong box" is sometimes used for safes that are no longer portable boxes but are installed in a wall or floor for increased security.
A toolbox is used for carrying tools of various kinds. The term implies a container meant for portability rather than just storage, for instance with hinged lids, clasps or locks, reinforced corners, and handles. Toolboxes are usually very sturdy, but unlike a shipping box containing dunnage, are not expected to fully protect their contents if the box is inverted or upended.