Most welding processes use acronyms as their name. For example "SMAW" or "stick" welding stands for Shielded Metal Arc Welding. Each arc welding process has the same root principal: fuse two or more pieces of metal together using an electric arc as a heat source. Once a "short circuit" is started, an arc is created. During this process the arc is maintained and controlled through the machine, welder, or computer depending on the process and application.
MIG welding is a "semi-automatic" welding process, in which the filler wire doubles as the electrode and is fed through the welding gun to the area to be welded. Once this electrically hot electrode meets its opposite polarity grounded metal, an arc is created and the wire is instantly melted into "weld." MIG stands for "Metal Inert Gas," meaning there is an electrode doubling as filler material and it is shielded by an inert gas so the molten metal isn't subjected to air, resulting in a brittle and weak weld. MIG is mostly used for production, and mobile welding, not really suitable for cryogenics or high quality welding.
TIG welding is a fully manual process. TIG welding is where the electric arc is jumped from a piece of tungsten to the weld material and a filler wire is slowly fed into the weld by the welder's hand drop by drop. The arc is either started by scratching the grounded metal or using "high frequency" electricity. There are different types of tungsten electrodes for different metals. In this process, unlike the others, the "heat" or current can be controlled by a foot pedal during welding, making the weld more pristine and high quality. That is why TIG is mainly used on semi-precious metals and cryogenics.
Another difference is the overall difficulty difference between MIG and TIG. A monkey can be trained to MIG weld. You have a lot more room for error with MIG. However with TIG welding you can sneeze, fart, or burp and it will show up in your weld leaving you to grind it off and do it again, which is a lot of waste: time, material, labor, and electricity. So, in a nutshell, each welding process is different, especially MIG and TIG. However, all arc welding processes have the same root principals, filler wire, an arc, and and some sort of supplied or generated gas shield to protect the molten welding metal from the air.