Even the “metric” measurements for firearms ain’t necessarily true measurements either. Lots of them get rounded off or simply depend on just how they made the measurement to start with, (land to land or groove to groove). In any case a bullet diameter is almost always going to be just a tiny bit larger than actual bore size for modern cartridge bullets.
Metric was too confusing for bullets, so we use both, and but neither of them are actually the diameter of the bullet, most of the time.
.223" is the same diameter as 5.56mm (which is 5.7mm across), but if you use 5.56 in a 223, it might kill you.
223 in 556 is fine, might fail to cycle.
Even the “metric” measurements for firearms ain’t necessarily true measurements either. Lots of them get rounded off or simply depend on just how they made the measurement to start with, (land to land or groove to groove). In any case a bullet diameter is almost always going to be just a tiny bit larger than actual bore size for modern cartridge bullets.