Varieties of Paintball Bags
Paintball gun bags tend to be the smallest, and the cheapest solution. They are primarily designed to store your paintball gun. Some may have additional compartments, but if you're only interested in a specialty case for your marker, this might be the solution for you.
Paintball gear bags come in a lot of different shapes and sizes, but most are designed to be far more full-featured, and come with room for guns, tanks, pods, maintenance and repair items, squeeguees, everything but the kitchen sink (and a couple of the larger ones might have enough room for one of those, too). Many gear bags, because of the size and weight of them, come with wheels, and if you're looking at a gear bag you might want to consider whether or not you want to physically haul all of your equipment before the game even starts, or whether you'd rather be able to wheel it around.
Paintball backpacks tend to be a median solution, essentially a stripped down version of a gear bag that's designed to go on your back, while still giving you more hauling capacity than a gun bag alone. Most of paintball backpacks will have room for a gun, maybe a tank or some pods, but depending on your loadout may not be able to store everything. If you're planning on wearing your harness anyway, or don't feel like you're going to carry around so much gear you need one of the bigger bags, backpacks offer a decent amount of storage without all the added weight, and greater mobility to boot.
Choosing Your Paintball Bag
The tote that's right for you is the one that's going to fit what you're doing with it. If you're just looking for a way to keep your o-rings, oils and allen wrenches handy at the field, a backpack keeps that all compact. If you just want to make sure your gun doesn't get scratched up, a gun bag will do that. If you're the kind of player who wants to bring two big jugs of water, an extra tank, maybe even a whole second load-out for a friend, then a gear bag is an absolute must. As always with paintball gear, you should figure out what you need, first, then use that to narrow down which bag you might want.