0.308-inches is the diameter of a 30 caliber bullet (or 'projectile' to be clear).
Cartridges like 308 Winchester simply use the full designation, where other cartridge names use the abbreviated 30 or 300 designation: .30-'06, 300 Win Mag, 300 Savage, .30-30, etc. But all use the same projectiles. 7.62mm military cartidges use the exact same bullet, with the exception of Russian cartridges. 303 British is also different.
If you're interested in reloading, get two or more of the published books on the subject: Lyman, Speer, Sierra, Hornady, Lee, Nosler, ABC's of Reloading. Pick any two. They contain just about all the learning you need.