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Overloading ammunition cartridges dates back to the 19th Century, when Smokeless Powder began to replace Black Powder as the gunpowder of choice. Smokeless Powder has far more energy density than Black Powder, meaning a cartridge of the same size would be much more powerful if loaded with the new powder. Although the revolvers of the time were usually not strong enough to handle this increased power, most pistol-caliber rifles were strong enough and thus the "rifle only" powder load was born. Eventually, rifle cartridges evolved away from that of pistols so both the term and the practice mostly disappeared.
In the early 20th Century, Colt revived the practice when they created the .38 Super Automatic. Colt's .38 ACP was a popular caliber, but Colt wanted to increase its penetrating and stopping power to make it more appealing to the US Military and Law Enforcement. The latter especially was finding the ACP coming up short in firefights with gangsters, who sometimes used body armor and often used their heavy carrs as cover. The .38 Super was simply an ACP with a higher pressure gunpowder load compared to the original.
Since the Super, many cartridges have received the overpressure treatment. Today, these generally wear the Plus P label to denote their higher load compared to more basic ammunition. Plus P can be dangerous, as it at a glance appears identical to standard ammo and use of Plus P in a weapon not designed for it can cause the firearm to catastrophically fail when fired. This is why Magnum cartridges are designed to not fit in standard weapons. Even for hardened weapons, Plus P will cause them to wear out faster. But the higher muzzle velocity and the extra lethality it represents is often found to be worth it.
Some games include ammunition upgrades, such as Call of Duty 4's Stopping Power perk, which could be rationalized as Overpressure Ammunition.