While it is often stated that the term "BB" originated from "ball bearing" or "bullet ball" (if it is made of plastic), this is not the case.[1] The original BB guns used the BB-sized lead shot for shotguns, midway between B and BBB size. BB shot was nominally 0.180 inches (4.57 mm), but tended to vary considerably in size due to the high allowable tolerances for shotgun shell use. Around 1900, Daisy, one of the earliest makers of BB guns, changed their BB gun bore diameter to .175 inches (4.45 mm), and began to market precision-made lead shot specifically for their BB guns. They called this "air rifle shot", but the "BB" name was already well established, and everyone continued calling the guns "BB guns" and the shot "BB shot" or just "BBs".
Subsequently, the term "BB" became more generic, referring to round shot (and sometimes non-round shot) of various calibers and materials. This included (and still includes) bearing balls, plastic round shot (such as used in airsoft), 0.177 caliber lead and steel shot, marbles, and many others. It should also be noted that the ubiquitous usage of the term "ball bearing" for any steel ball is technically incorrect. A ball bearing is a mechanical bearing constructed with a multitude of bearing balls.
Source: Wikipedia