An e-cigarette “Mod” in it’s simplest form is a battery tube/box.
It’s a tube/box that holds a rechargeable battery with a connection to attach an atomizer. This could be a mechanical mod or regulated mod. The combination of a mod and atomizer would give you a functional e-cigarette mod.
Variable wattage devices automatically adjust the voltage output based on the resistance of the coil inside the atomizer on the device. Other features might include resistance checking, battery level displays and screens.
Mechanical mods generally don’t have voltage regulators or lights. Voltage output from mechanical mods will be directly related to the actual output of the battery(ies). This means that there is generally a sloping curve of power output from the mod as the battery drains.