I'll do the best I can with the limited knowledge I have on the subject, but you're welcome to ask any questions you might have. If I do not know, I will be able to help find the answer for you.
Ok, we will start with Variable Wattage (VW). Variable Wattage is very simple in that you tell the mod what Wattage you would like to vape at, and it adjusts the Voltage going through the coil to match your preference. There are a couple different ways of achieving this with software, but they have very similar results. The end result will always be that you tell the mod the number of watts, and it will calculate the math and lower or raise Voltage accordingly.
Temperature Control (TC) is a totally different animal and is much more sophisticated. In most mods that do TC, you have control over the amount of Watts delivered as well as controlling the final, and holding temperature of the coil as well. This is achieved by using certain kinds of wire whose resistance(ohms) changes measurably when its temperature changes. Ex- Ni200, Titanium, and Stainless Steel. When Voltage is applied to these coils and they increase in temperature, the computer inside your mod reads the resistance change and calculates the temp of the coil itself, and adjusts accordingly to the temperature that you set it to. This is very helpful because when your cotton starts to dry out, or run out of juice, there is nothing to keep the temperature in check and it will raise very quickly. The mod will see this, and reduce power to keep your cotton from burning up, or getting a dry or burnt hit. Some people swear by TC, but I'm old fashioned and will probably always just use VW, even with Stainless Steel. I've been vaping long enough that I can tell long before my cotton has gotten dry, because the taste will become muted, or lacking. A person new to vaping though may benefit greatly from the ability to pay less mind to the level of juice and be comfortable knowing that there is a system in place to keep them from the dreaded dry hit or burnt hit.