There are differences between 7.62 and 308, but the dimensional differences are insignificant compared to the huge gun to gun chamber differences in the guns of both calibers.
7.62 is made to a set of specifications that includes some issues that 308 does not address. The powder is required to have a lower muzzle flash. Commercial ammo specs are silent on that point. The big difference is that the case head for 7.62 is typically harder (stronger) to resist the violent extraction of an automatic action. When 308 brass gets chewed up by extraction, this is sometimes ascribed to higher pressure. Not so. The pressures of the two flavours are about the same. 308 brass is often softer - that is why it gets chewed up.
7.62 also has port pressure specs, which 308 does not. This can cause 308 ammo to over gas a M14, especially if a heavier bullet is used (slower powder means higher port pressure.)