For the Derailler, if it's the front then you probably mean...
Bottom pull or top pull which is the direction the cable is routed to move the derailler. If it's a top pull derailler, then the cable probably runs along the top tube and then down to the derailler. If it's a bottom pull, then the cable either runs down the downtube and under the bottom bracket like a road bike or along the top tube to a pulley below the front derailler and the up to the derailler. There is no real difference other than the fact that by using a top pull derailler with cables routed high, there is less chance they will be mucked up with mud or water.
If you're talking about the rear derailler, then you may mean rapid-rise vs. regular shifting. In rapid rise, the shifting is effectively opposite what it is on a road bike. By tightening the rear cable you shift to a harder gear and by loosening the rear cable with a shift you shift into an easier gear.
Hydraulic disc brakes are more expensive, and in my opinion, more reliable than cable discs. They are more difficult to set up, but once you get them set, they are pretty much maintenance free with the exception of changing out the pads or the fluid if it begins to leak. The downside is that if the fluid leaks in the middle of nowhere or in a race, there's little you can do to repair it that I know of (although you can probably use mineral oil or regular DOT brake fluid in some of them). Cable discs will be more prone to being affected by water or mud, but they are less expensive and set up can be a little easier (ie less messy). Many folks also believe that you get better control and modulation with hydraulic brakes.
Brandon Marsh - Website | @BrandonMarshTX | RokaSports | 1stEndurance | ATC Bikeshop |