What is TIG and MIG?
TIG - Tungsten Inert Gas; also called GTAW -- Gas Tungsten Arc Weld, but nobody calls it that except the American Welding Society (AWS)

A small torch with a tungsten electrode is used to make the arc inside an envelope of an inert gas, usually argon or some argon mixture. A filler rod is manually introduced to complete the weld. The resulting weld is very pretty and usually requires no further finish. It is used mostly for welding sheets of mild steel, stainless steel or aluminum. The better machines have a foot control and a high frequency arc starter. Any sizable stick welder can be retro-fitted to do TIG welding, but without the foot control.

MIG - Metal Inert Gas

MIG and wire feed are the same thing. In this process, a consumable wire electrode is fed from a spool to the torch where the weld occurs inside an envelop of pure carbon dioxide, pure argon or a mixture of both. The weld continues as long as the operator has the trigger depressed and there is something to weld. This process is very fast, easy to learn and results in fairly good looking (better with argon) and strong welds. Most production welding of mild steel is now done with MIG welding. There is no slag to chip, but there is a slight thin coating of a glassy material that probably should be wire brushed off before painting. MIG welding can be used for thin or thick materials and is commonly used on mild steel, stainless and aluminum. Some common features of MIG machines are spot welding and stitch welding of sheet metal.