MIG- is metal inert gas. It means simply a wire feed (the consumable electrode) welder with a inert shielding gas, such as argon or CO2. Meant for more production work, easy to use and get results.
TIG is tungsten inert gas, "An electric torch" so to speak. A torch holder that has a nozzle holding a tungsten electrode(non-consumable), that has a flowing shielding gas such as Argon/CO@(or in rare cases pure Helium,Big $$$$) Meant for precision welding and for nice neat work. Typically really strong.
Edit- I see you have 2 welding related posts, I think you might have to do a little more research, out side this forum on this subject, as there will be some info we wont be able to fully explain to you, in which we will most likely be referring you there any ways.