The early history of airgun calibers in the US is complicated with a lot of variation and no real standard. All the barrels were smooth bore, intended for slugs and darts. The slugs with a tuff of cotton on the rear is intended to make it possible to shoot in an oversized barrel. These guns also appeared intended more for use in shooting galleries than for individual use.

The pellet did not exist in the US until the introduction of the BSA. The BSA was the first rifled airgun sold in the US. The next rifled airgun in the US was the Crosman in 1923. The Crosman rifled .22 stood alone among US manufacturers until the late '30s when Benjamin finally introduced their own rifled .22 models.

So, at least in the US, the .22 pellet standard was started by the BSA rifle which was picked up by Crosman in 1923 and then confirmed forever by Benjamin some 17 years later.

The .177 caliber didn't really come into existence in the US until the mid '30s when Benjamin introduced their rifled pistols in that caliber; Benjamin .177 caliber pellets being imported from England. Crosman didn't produce a .177 rifle until 1940. So, again, the .177 caliber pellet standard came to the US from England.