A "stick" arc-welder is the kind most people think of when they picture a welder; the person holds an electrode that has a long skinny stick poking out of it that they contact the metal with. All the sparks and action happen at the end of the stick. The stick's the electrode; the arc that melts the steel forms between the end of it and the metal you're welding. The electrode is consumed by the process so you have a container full of sticks and you keep replacing them as you work. It's tricky because you you have to sort of float the electrode over the surface of the steel; if you actually touch the steel, the end of the electrode fuses to the steel and the arc stops. You have to break it off and fire it up again. I suck at stick welding; I fuse that electrode all the time and it's just aggravating. The real strength of it is that you get a very deep burn welding that way; you can weld the really thick structural steel.
The other, easier type of arc welding is with a wire-feed welder (MIG welding is a sort of wire-welding). Instead of sticks, the electrode is a spool of steel wire inside the machine that feeds through the handle and thus replenishes itself while you weld. It doesn't fuse as often if you have your feed speed and power settings adjusted correctly; so it's a lot easier if you're an infrequent weldor like me that doesn't weld often enough to really develop a talent for it LOL. With a MIG machine (Metal & Inert Gas), there's a tank of inert gas that flows out the nozzle where the wire pokes out, so the arc is happening in its own little puddle of inert atmosphere, so the molten metal doesn't oxidize and slag doesn't form on the weld (with stick welding, you need a little steel chipping hammer to chip and scrape the welds clean). When you get good, you get clean, slagless, almost shiny welds that look like fresh-squeezed toothpaste. Very tidy.
What type of welder you want depends on what you'll be welding. 240V machines are much more powerful (obviously) than 120V ones, so you can weld thicker steel. Stick-type welders are less expensive machines (fewer moving parts) and enable you to weld heavier stuff, but it really helps to get training because their trickier to use. MIG welders are much more expensive but easier to use, give prettier, cleaner welds, and enable you to work on thinner, smaller steel without burning huge holes in it. I have a smaller machine than TD because I never weld anything over 3/16" or 1/4" thick. But on the flip side I can crank down the power and weld very thin sheet metal; you could never do that with a stick arc welder. For haunt and hobby purposes you can get by with the little mini MIG like I have; a bigger one like TD enables you to weld on really heavy stuff like car frames.