With Arc (stick) welding the electrical flow goes through a hand piece that holds a welding rod. The arc of electricity between the work piece and the end of the rod melts the rod into the host metal. Flux is one component that makes up the welding rod.
MIG stands for Metal Inert Gas. Electricity flows through a wire that is fed from a spool and through a gun. The tip of the gun also has accommodations for inert gas such as Co2 or Argon (or a mix of both) to shield (wash over) the weld. If the gas did not flow around the weld then oxygen would contaminate and pretty much render the joint useless. Gasless MIG uses wire that has a built-in flux that does the shielding..as opposed to gas.
TIG stands for Tungsten Inert Gas. Here you strike an arc with a hand piece that has a tungsten tip. You then feed the welding rod into that arc to complete the welding process. Inert gas wash the work area to prevent contamination.
Each of these is dependent on an arc to effect the weld.
Stick(arc welding)
MIG
TIG
