Mig is a wire fed process that uses an Inert (hence the I) gas to shield the wire, like argon. Sometimes the gas is ert (or active) like co2, and thus you might hear the term MAG in place of MIG (for metal Active gas), but mostly MIG is used for simplicity. Folks also often refer to flux core as mig, but it really is not. Flux core is just wire with a flux in the middle that shields the puddle when it burns. All these methods (an some other processes) are performed in pretty much the same way. You feed a wire from a machine, through a big, thick hose to a gun that squirts it onto the thing you want to weld. The wire is electrified and a circuit is completed at the weld (somehow). The "somehow" differs based on gas, amount of current and other variables, but that's not so important when learning the basics. In fact, I have just recently gained a better understanding of this stuff after welding for a pretty long time, at least in dog years.
Tig, on the other hand, has an electrode, but the electrode doesnt get used up in the process of welding. It's much more like a gas torch (oxy/ace) in the way you weld. You heat the metal with a (sometimes) very precise plasma-like flame and add filler in the form of a rod using the other hand. Often, you use real-time amp adjustments to control the heat for better results. Tig, as a process, can weld just about anything short of peanut butter (or in your case, maybe, Vegemite), but it's a bit harder to learn, requires some pretty good hand-eye coordination, and is a good bit more expensive to do if you truly intend to weld everything under the sun. Mig isnt as hard as stick.
DC is less dangerous, pretty much always, so dc tig, stick, mig are all less dangerous than ac anything.
The main difference I see between mig and tig is that in mig (loosley defined), the wire IS the electrode and the filler. In tig the electrode is NOT the filler, unless you do something really wrong. Other important differences that you don't exactly see: Tig can be either ac or dc, mig is pretty much dc, as far as I know. Tig uses constant current (CC), where mig uses constant voltage (CV). I only understand the very basics of this, so if someone wants to add something about that....
When you get down to the basics, the definition of each welding process is mostly determined by a particular combination of heat, filler type and method for shielding from the atmosphere. In other words, all the different processes are usually described based on each one's particular methods used to get the heat, add the filler, or shield from the atmosphere. There are probably some exception to this, but I can't think of any right off.
You shouldnt feel left behind by using stick. It's still a very viable method for many things and in some cases the best method. There is a good reason that almost every welder on the market (except wire fed only) have stick mode. It's not for backwards compatibility with old weldors. It's because it's still a preferred method for lots of stuff. One thing i really like about stick, is that if you drop a box of sticks, nothing happens. If you drop a roll of wire, all hell breaks loose.