7.62, 7.63, 7.65 mm???

[unspellable]

As I recall, the 308 Winchester has a 308 groove diameter, more or less standard for 30 caliber barrels in the US. The 307 is the rimmed version of the 308 and was called the 307 to distinguish it from the 308. Which gets us right back to the name may or may not correspond to either the caliber or groove diameter.