In the vape world, “mod” usually refers to any unit that supplies power to the tank or atomizer. A “box mod” is usually referring to a device that uses two batteries or more and is generally shaped like a box.
The term “mod” comes from the early days of vaping when the units for vaping were everyday modified items. They were created from things like modified flashlights and other household items to use for vaping. Today mods come in all shapes and sizes. A “mod” can have an internal battery or use external rechargeable batteries.