Cartridge nomenclature is some very tricky business and manages to baffle the majority of firearm owners.
The American system is particularly vexing, though the majority of American cartridges do provide the caliber the diameter of the rifle bore first in the name. For example, a 30-06 is a .30 caliber round, meaning that the bore diameter is .3 of an inch. The remainder of a cartridge’s name isn’t so formulaic. In the case of the 30-06, for example, the name comes from the fact that it’s a .30 caliber round that was first designed in 1906. The 300 Savage is another .30 caliber round, though “Savage” comes from the name of a rifle manufacturer. Adding to the confusion is the fact that so-called .30 caliber rounds actually measure .308 of an inch. Thus, a cartridge called the .308 Winchester is, in fact, the same caliber as a .30-06; like the 300 Savage, it carries the name of a rifle manufacturer.
Things are a little clearer with cartridges that were developed in the days of black powder, as the name carries the caliber and the original grain weight of the charge. A designation like 45-70 would have indicated a 45-caliber bullet with a 70-grain charge of black powder. Sometimes you’ll see an additional number on the end. For instance, a 45-70-405 would be a .45 caliber bullet weighing 405 grains and charged by 70 grains of black powder.
The European stuff is simple, which should be expected from a continent that embraces the metric system. A 7.62×39 is a 7.62mm bullet with a case length of 39mm. Across a wide variety of European cartridges, there is little or no variation in their system.
And then there are the “wildcat” cartridges, which find their genesis as experimental cartridges designed by tinkerers and ammunition manufacturers who blended available cartridges to make Franken-ammo. For instance, the 7mm-08 comes from loading a 7mm bullet into a .308 Winchester casing in a process known as “necking down” (i.e., reducing the neck of the case to accommodate a smaller bullet). Some of these wildcat experiments were successful in filling gaps between standard cartridges and are now produced by major ammunition companies.