MIG welding (acronym for Metal Inert Gas) is properly defined by the American Welding Society (AWS) as GMAW. (Gas Metallic Arc Welding)
And TIG welding (acronym for Tungsten Inert Gas welding) is properly defined by the AWS as GTAW (Gas Tungsten Arc Welding).
The gas flow rates are different for several reasons. They are entirely different processes which use entirely different equipment!
The sole purpose of the flow rate is for the gas to cover/protect the molten weld pool from getting contaminated due to a chemical reaction with the various gases in the atmosphere. If the flow rate is insufficient, the atmosphere will contaminate the weld pool. If the flow rate is too high, the turbulence of the covering gas will itself draw in the atmosphere and expose the weld pool.
Even within each process (MIG or TIG) there is a wide variation of gases used as well as differing flow rates for the sizes of wire, cups, tungstens, orifice openings, amperages, voltages, ambient conditions, and base materials being joined.
Good luck and have fun!