TIG welding is the electrical equivalent of GAS welding, when you weld using a TIG welder the Arc (The Heat-source) which creates the molten pool of metal (weld pool) is separate from your filler rod (Welding Rod) (Because its in your other hand) it allows you to have a great deal of control of heat penetration and how quickly you cool your weld pool by inserting the filler rod into it to join the two pieces of metal together.
MIG or ARC welders use the filler rod or wire to carry the arc and fill the weld, although its possible to slow the feed of the MIG and/or change the angle of the torch or turn up the current, you don't have as much control as the TIG. A good welder can see and judge the optimal heat to create a deep weld to ensure good strong weld penetration but he or she is restricted by the welder to a certain degree.
The top weld (Up to the surface) could be filled in with MIG ARC as your not having to push the heat as deep.
Hope that answers your question. (Its years since I had my Welding Qualifications)