Headers come off of the engine, specifically the heads. There are several different kinds: Long tubes (where the primaries (individual pipes coming off of each exhaust port) are long
), unequal length shortys (where the primaries are rather short, this is the factory kind of headers), and equl length shortys (where the primaries are still short, but all the same length).
Mid-pipes come in basically 3 different variations: H-pipe (where the crossover makes the shape of an h), prochamber (basically an h-pipe, but these are proven to make more power), and an x-pipe (where the crossover makes the shape of an x). They come either with cats, or no cats (i.e. O/R (off-road, no cats are illegal on teh streets), so o/r x-pipe means an mid-pipe with an "X" shaped crossover with no cats. Oh yea, the stock piece is a catted h-pipe.
Then the cat-backs are everything from the mid-pipe back, they include flowtubes (pipes between the mid-pipe and mufflers), mufflers, and tailpipes. There are about 3904809834 different kinds of catbacks. Dumps are simply when you "dump" the exhaust right after the muffler, instead of having full tailpipes run out and exit the rear of the car. Dumps make it a lot louder, and some people complain of the exhaust smell getting into the car.
Hope this cleared up your questions, feel free to ask more.
-Chris