Preamp vs. Power Amp Distortion
Alright, I'll try to make this as simple as possible.
Distortion is caused by "clipping," meaning when an audio signal gets too loud for *something* to handle, the sine wave that is usually rounded hits the top and flattens out. Our ears pick this up as what we know as "distortion."
Generally there are 3 places we're concerned with where distortion can occur, and it all depends on where we're making the signal too loud (overdriving). The first place it can happen is the preamp. This means that either your signal is too strong going into your amp, or you have the preamp volume or gain overdriving the signal. This is the most common type of intentional distortion, and usually gives you more shrill, defined, rock distortion (unless you're overdriving the input, which usually gives you some nasty fuzz or chunky distortion).
The second place is the power amp. If you get distortion here, it means you're pushing your amplifier stage past the point where it can create clean sound. A lotta people wonder why a 50 watt tube amp will get louder than a 100 watt solid state. The main reason for this is that tubes can be pushed far more than what they are rated at, where-as solid state amps have a very solid ceiling. However, when you start pushing amps over their rated level, you get clipping, and this creates another type of distortion. This type of distortion creates a sound kind of in between your more shrill distortion and crunch, and usually comes into play in combination with preamp distortion.
The final type of common distortion is speaker distortion. This occurs when your amp is rated close to or more than your speakers (quality speakers are usually rated in watts and that rating is supposed to represent the amount of power they can take without creating audible distortion, however many companies do a lot of numbers fudging with this and distorition can be achieved at much lower levels than rated). This is where you get your crunch distortion. Generally, you do not want this distortion, as it will wear out and could blow your speakers.
Anyway, these are very generalized definitions. Modern amps mimic and create distortion in many, many different ways, and pedals also try to recreate the many different types of distortion. Usually though, people focus mainly on their preamp distortion. Speaker and amplifier distortion come into play when you go to play live and are forced to turn up your amps. It is very important that you make sure your rig is going to sound good at high levels BEFORE you go on stage, because a setup that sounds great at practice can sound like absolute poo when you're cranking it 3x as loud live.