TIG welding stands for tungsten inert gas and uses a tungston electrode that is not consumed in the welding process. Used for stainless, aluminum, copper, etc it is a specialty welder.
MIG welding stands for metal inert gas and is more commonly called a wire-feed welder. Has a roll of wire(depending on metal being joined) that feeds out the tip for welding. This type of welder is much more common and can be used for metals other than steel, but is widely used to weld light steel.