Confused? You will be.
In short, caliber is the measurement of the internal bore of a barrel. And that is about where the simple description ends. You see, because most modern barrels have rifling, there is actually two places you can take this measurement from. The lands, which are the high points in the rifling, or the groove, which are the low points. Generally, the US is going to measure from the groove, while the rest of the world will measure from the lands.
Generally, where a caliber bore measurement is given in inches, the inches can simply be replaced with ‘cal’. For example – .308 cal is a bullet generally .308 inches in diameter.
However, imperial isn’t standard in a lot of the world, so metric can also be used. For example, the .308’s close relative, the 7.62×51mm NATO is a 7.82mm projectile in a 51mm lengthed case for a barrel with a land to land bore of 7.62mm. However, because just using one or the other would be too simple – you also have manufacturers putting out hybrids – i.e. the 7mm-08. This is a .308 (imperial) cartridge, necked down to fit a 7mm (metric) bullet.
Then we have wildcat and homebrew cartridges that really just get named however the maker wants.