A garden gun is a gun used for pest control in the garden or grounds. It is large enough to kill snakes, rabbits, rats, and other small pests, but won't easily take down a deer or a human.
These are traditionally small cylinder bore shotguns, firing low gauge shells, most often a .410, a 9mm Flobert (EU), or a .22 rimfire (US). They are generally effective up to a range of 15 to 20 meters, but the low velocity shot limits ricochets when firing at close targets. This makes them comparatively safe to fire inside barns and sheds, limiting their ability both to punch through the walls and decreasing the risk of collateral damage from ricochets.
A small caliber handgun used in the same fashion may be called a kit gun, as it is often included in a camper's kit.