Oxy/Acetylene welding is kinda like TIG welding. you heat the parent metal and add the fill rod as you go. Stick welding (electric arc welding and gas-less mig welding) run current through the filler metal and thats what creates the heat for the weld. Like mike said, stick welding and gas-less mig welding spatter a bit, but can still produce good welds. Regular mig (metal inert gas) welding has a shielding gas that purges all the impurities from the weld area and makes a cleaner weld. Tig welding (tungsten inert gas) uses a "torch" to heat the metal. the torch has a small needle like tungsten tip that sticks out of the end and has a shielding gas (usually pure argon) that flows from the tip as well to keep the molten metal in a pure atmosphere. An electrical arc goes from the tip of the tungsten to the parent metal and creates a puddle of molten metal. you then add filler metal, or fill rod, to the puddle to make the weld. Tig welding is by far the cleanest looking weld you can do, but it also requires the most prep work.
If you have any other questions, feel free to ask