Cheap & dirty answer~
In Stick process- on steel
Many electrodes are current specific eg 7018 is a DC rod, don't run for **** on AC. 7018 AC runs fairly well on AC, but it ain't worth writing home about.
6013 will run AC, DC or DCRP handles nicer on DC than AC, but there is no way in hell to run vert up with 6013.
Contrary to the bullcrap spouted by a lot of people, it is totally possible to run overhead on AC with the proper rod. In my world if you can't run an overhead pass of 6013 overhead you ain't a weldor. 90% of the people who claim to be weldors can do it with DC, but they ain't got a hope on an AC machine. Once again, the weld ain't in the machine, it's the man or woman since I did teach a 16 year old girl to do it a while back.
When you run into a piect of steel that is magnetic, DC will drive you nuts, and often switching to AC will let you burn the weld in.
Carbon arc will run nice on DCRP, and lay everdure down slicker than snot on a doorknob either flat or vert. You can't strike and hold an arc with carbon on AC tosave your *** unless you're flying a 2 carbon torch.
A 2 carbon torch on AC works real well to loosen rusted and or frozen nuts. Try it with DC and you got nothing but a headache.
When you get into Stainless, most electrodes tend to be DCRP. Some AC electrodes are available, but DCRP delivers a nicer deposit.
TIG process-
Steel, stainless and copper are pretty much DC processes. THICK Aluminum can also be welded with DC TIG, if you go to Helium shielding. Most aluminum is welded with AC with constant hi frequency added for cleaning. When you get into inverter machines, square wave machines, sawtooth machines it's possible to do some very interesting things with the arc as far as cleaning and penetration, as well as hanging globs of molten metal in mid air.
MIG machines- Manufacturers are still developing new trick power suplys every day for aluminum and other exotics. I played with a MIG setup for aluminum a few months ago in the Dealer's lab, and it impressed me. The power suply is computer operated, and designed for robot operation. The machine started the weld with DC Hi Freq superimposed to establish the arc, then switched to sawtooth positive wave only for the run, and back to DC at the end of the deposit for crater filling.
MIG for basic steel is pretty much DC power suply constant voltage.