Variable Voltage refers to electromotive force being pushed through the atomizer. That sounds scary but it is not, it is actually incredibly simple. Think of this as a manual car, when you put an atomizer onto a device and use variable voltage you will need to adjust the voltage yourself depending on what resistance atomizer coil you have. Too little and it won't heat up quick enough and you will struggle to produce any vapor. Too much and you run the risk of prematurely burning out your atomizer head. As long as you know what resistance your atomizer coil is, and the preferred voltage you can just adjust your settings and vape.
Just remember, if you change your atomizer coil to a different resistance the settings will need adjusting each time.
Variable Wattage refers to the power produced by the electromotive force. Once again this sounds extremely technical. Think of this as an automatic car. Whatever wattage you set your device to it will give you that wattage by automatically adjusting the voltage for you. For example, if you set it to 10 watts, no matter what resistance atomizer coil you have in your tank, it will give you 10 watts by adjusting the voltage for you.
Nice and easy, you technically don't need to adjust this every time you change your atomizer coil or swap tanks, find a wattage you like and stay there. Although as with everything in vaping there are some exceptions to the rules.