PAINTGUN PRIMER
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Paintball guns are air guns that shoot a .68 caliber ball made of water soluble paint. The shell is the same stuff as the fill, but cured into a container shape usually and hopefully very round. They all use expanding gas to send that ball forth.

Most of the time you'll see what are called Constant Air bottles attached either directly on gun, or with a Remote system which is a simple hose running from the bottle to the gun. In remote set-ups you carry the bottle in a harness. Guns are set up in one or the other way. The advantage of an On-Gun set up is that the gun is more mobile and you can put it wherever you need to put it without much hindrance. The Bottle can double as a shoulder stock, giving the gun more stability and thus more potential accuracy.
The disadvantages are that it adds length and weight to the gun, which then may hinder the speed with which you can bring the gun to bear on your target. With Co2 set-ups there is less distance between the bottle and the valve, which means that there is less potential for the co2 to expand and thus the potential for less consistency of shooting velocity.
Remote set-ups allow for more freedom to swing the gun around both by virtue of making the gun lighter, and shorter. It can also help to balance the gun out a little.
The longer hose allows co2 to expand more, thus keeping the volatile Liquid out of the gun's valving. However, a remote hose is a leash on the gun, and it can and will get snagged by twigs, branches, and other protrudences on the field. Also without a shoulder stock added to the gun, longer range shooting may suffer.
Finally, a remote setup places a bottle in a harness on your back, this can be tiresome and gives the opposition a larger target profile to shoot at.

All Paintguns have some sort of safety that stops the gun from triggering. Some guns have the safety removed for performance reasons, in those cases other measures are used to ensure a gun is safetied when not in play.

There are several ways to classify Paintguns, but in the broadest sense, you have Pump Guns and Semi-autos. The two definitions refer to the manner in which the gun is recocked. Pump guns use a pump handle to recock, Semi-autos recock as a part of the gun's essential makeup. Obviously this means that a pump gun shoots at a slower rate of fire than a semi-auto, also there become certain physical limitations with a pump that you don't have with a semi, such as shooting with a pump while laying tight to the ground. Since pumpgunning is a two handed operation, you can see laying flat can be tough with a pump gun. On the other hand, since much a in a firefight calm accurate shooting can be key, being forced to a slower ROF may help a player take better shots.
I know that when I play with a pump gun against semi-autos, I am forced to play a better game, and usually it shows.