Ahhh, That answer could take all day. so here is the short answer
They all heat metal to its semi liquid state where the material can reform into a new shape. Arc welding heats the metal up where the contacts touch. Gas uses heat from a neural flame.
Most MIG machines make the arc contact with a consumable wire that also becomes the metal filler.
Stick, like MIG, but can do thicker stuff. the rod is the consumable. it has a flux that gasses off to keep the weld clean.
TIG uses a tungsten electrode that is not quickly consumed to make the arc, and the user fills in metal (wire) the other hand.
GAS flame heats the metal to a cherry red state. The user added metal to the weld "pool" like the TIG to make a connection.
MIG and TIG use a shield gas at the tip to keep oxygen from the weld pool.
Have kilt, will travel...