The Spiegel and the Lincoln use welding rods. That technology is referred to as SMAW (Shielded Metal Arc welding). The stick electrode is used up/deposited as you weld and the molten pool is protected by a shielding gas cloud produced by the flux coating on the rod burning as the rod melts.
MIG (Metal Inert Gas) welding is what your newer welder is doing. A spool of wire is fed thru a lead and gun, melted by and arc and deposited. Shielding of the molten pool is either accomplished by Inert gas being fed thru the lead from a bottle or by using special wire that has a flux core.
TIG (Tungsten Inert gas) welding uses a tungsten rod as an electrode and creates an arc between the tungsten and the work metal to create a molten pool. Wire rod is fed into the pool by hand to act as filler rod. Shielding gas from a tank is introduced thru the lead supplying power to the tungsten electrode. This process has some slight similarity to oxy-acetylene welding in procedure and technique.