Well, that's your rundown of the different types of barrels, now for some terms:
Porting: The holes towards the end of your barrel. These vent excess gas, causing the marker to be quieter. Too much porting can be difficult to clean, as well as leading to decreased air efficiency, as porting will slow down a paintball a bit.
Rifling: A concept in which the inside of a barrel is not smooth, but has specially designed ridges, which, in concept, would spin the paintball, giving it better accuracy. Due to the composition of paintballs, rifling is NOT practical for use in paintball barrels.
Velocity: This is how fast a paintball travels, propelled by a gas. This only has to do with barrels because the paintball accelerates in the barrel. A paintball typcially needs about eight inches of unported barrel length to reach its velocity of 280-300 fps efficiently.
Efficiency: You'll hear this a lot when it comes to barrels, it means how many shots a marker can get out of one tank fillup.
Bore size: This is how big the inside of the barrel is, as well as the size of the paintball. A typical size is .689.
Paint to barrel match: This is how well the paint fits the barrel. As I mentioned before, this isn't a really major issue unless you have a closed bolt marker.
And some general barrel info, as this comes up a lot:
Barrel length is totally preference. A 16" barrel will not be more accurate than a 10" barrel, or vice versa. Longer barrels (assuming that the amount of porting is affected by length, which it almost always is) will be less efficient than their shorter counterparts. Depending on how you play, this is my recommendation as to what barrel length you should use: Speedball, on a regular field made out of tires and spindles and stuff: 12". Hyperball or Airball: 14"-16", so you can push in a bunker or get into the hyperball bunker's grooves. Woodsball: 14"-16", so you can put your barrel through some brush to get a good, protected shot.
Bore sizes are up to you. If you always use the same paint, I'd get a bore size a little bit bigger than the paint is supposed to be, so that way if a case is swelled you don't have a major problem on your hands. .689-.691 seems to be the best bet for something open bolt.
A few notes on "gimmick" barrels:
The Tippmann Flatline for either the 98 or A-5 is designed to put a backspin on the ball, therefore giving it greater lift, resulting in greater distance. This works nicely in theory, however the extra distance isn't effective distance; the paintballs are moving to slowly to consistently break on target. They're moving so slowly that they're very easy to dodge, and people have been known to catch paint shot out of a Flatline towards the end of its range.
Any barrel over 16" really serves no purpose, and seems to exist only to appeal to the "paintball sniper." Obviously, since no marker will shoot further than any other (except for Flatline'd Tippmanns, Z-Body 'Mags, and markers with the Undertow bolt), there is no true sniper in paintball. There are players who may use stealthy tactics, but nobody can take one shot from a football field away and hit. The longer barrels really are just more cumbersome and degrade the performance of the paintball marker.
Some helpful links:
PBR's official paintball size chart. Explains the bore sizes of different paintballs
Otter's guide on paintball barrel bore sizes. Really helpful!
Lots and lots of versus threads. Check here before making a thread like Barrel A vs Barrel B
Different barrel kits compared. Not an excellent thread, but it's not bad.
If you find any errors or omissions, or would like to see something added or changed, PM me with what you think! Thanks guys.
Super-helper people: CoolT