many of us do not camp at "campgrounds"...
My intention when camping is not to be surrounded by other people, but to get away from other people. Granted, owning property or having friends who do, makes this a little easier, but there are quite a few public access areas throughout the U.S. that are quite secluded yet accessible for camping, hiking, and even hunting.
A camp gun means different things to different people, depending on the circumstances. For me, it is typically a .22LR revolver. Also commonly referred to as a "kit gun", as others have mentioned. Uses range from general plinking and enjoyment to putting rabbits and squirrels into the stew pot, and in some cases for defense against predators, both two legged and four.
Maybe I "rough it" a bit more than others, but when I and my hunting buddies are out in the field, we travel pretty light. We take along a few niceties, but for the most part, if there is meat in the stew, it is fresh game, often taken with a kit gun. Because I hunt primarily with a handgun, a .22 rifle is often in my gear, as well as a .22 revolver. The idea of a "kit" or "camp" gun, in my opinion, is to be lightweight, and easily portable.
JW