Multiple names can be used to describe the same welding process because they are common slang terms. It doesn't matter what name you use, as long you know they are the same. Let me explain in this post.
TIG welding (or TIG) is an abbreviation of "Tungsten Irt Gas", but the proper name is "Gas Tungsten Arc Welding", commonly abbreviated or referred to simply as "GTAW". It was also known as "HeliArc" back in the day. GTAW, a joining technology, uses a constant current power source.
TIG uses a torch with tungsten in it to create an arc. To protect the weld surface from the air, the torch has shielding gas running through it. TIG works by creating an arc and then adding filler metal to the joint. This filler metal is available in wire form and can be easily cut to any length.
MIG welding (or MIG) is an abbreviation of "Metal Inert Gas", which is also known as "Gas Metal Arc Welding" and "GMAW". MIG is a term that derived its name from the original shielding gases used, which were either Nobel or inert gasses. The gases used today vary and the official name of the process has been changed to Gas Metal Arc Welding.
The most common term for MIG welding is "Wire Wheel Welding". This involves feeding solid filler wire through a wire feeder to the weld joint. The wire feed is connected with a constant voltage power source that causes the arc to melt wire when it hits the joint. The shielding gas must be fed through the system before the wire can create an arc.