Commercial .308 Winchester ammunition came first. The two ammunition types ended up differently.
Similar to the 5.56 NATO versus .223 Remington comparison, the difference between .308 Winchester and 7.62 NATO is in the chamber, but it’s in a different location.
The difference between these two calibers isn’t the throat; it’s the headspace. NATO is substantially longer.
Although there are different pressure-testing standards used by NATO and SAAMI, commercial .308 Winchester ammunition is loaded to a maximum higher-pressure than mil-spec NATO.
It’s safe to shoot NATO rounds in a .308 Winchester chamber, and .308 commercial ammo in a NATO chamber.
The difference is in what comes back out. The cartridge case for either caliber will be stressed. The softer, thinner commercial case might be deformed.
As for numbers, SAAMI spec headspace for a .308 Win. is a minimum (shortest allowable or “GO” figure) of 1.6300 inches, and a “reject” (too long) figure of 1.6340. Well, the number given as a minimum for NATO is 1.6380. The “reject” on NATO is 1.6455.
It’s also the reason NATO cartridge case specs call for considerably thicker-walled brass and associated hard alloy. It has to endure that much more expansion. It’s a big reason not to purchase “surplus” 7.62 brass for reloading. That’s the standard advice in the reloading community. Cases fired through an actual NATO chamber will be patently worthless to anyone owning a .308 Winchester chambered firearm. They will be blown beyond all reasonable use.
If you are a handloader for a firearm with a 7.62 NATO chamber, get a cartridge case headspace gauge and subtract 0.004 inches from the spent case reading to use as a figure to set your sizing die (case shoulder set-back). So, be sure not to take it down to .308 Winchester specifications, or it’s liable to break on the next use. Actually, break.