.308 Win is loaded to higher pressure than 7.62x51 (but the opposite is true with 5.56x45, as it's higher pressure than 223).
This gives good explanation (just scroll down), I've taken an excerpt:
http://www.accurateshooter.com/cartridge-guides/308win/
.308 Win vs. 7.62×51–The Straight Scoop
Before we go much further, we want to address the oft-posed question “Are the .308 Winchester and 7.62×51 NATO one and the same?” The simple answer is no.
There are differences in chamber specs and maximum pressures. The SAMMI/CIP maximum pressure for the .308 Win cartridge is 62,000 psi, while the 7.62×51 max is 50,000 psi. Also, the headspace is slightly different. The .308 Win “Go Gauge” is 1.630″ vs. 1.635″ for the 7.62×51. The .308′s “No-Go” dimension is 1.634″ vs. 1.6405″ for a 7.62×51 “No Go” gauge. That said, it is normally fine to shoot quality 7.62×51 NATO ammo in a gun chambered for the .308 Winchester (though not all NATO ammo is identical). Clint McKee of Fulton Armory notes: “[N]obody makes 7.62mm (NATO) ammo that isn’t to the .308 ‘headspace’ dimension spec. So 7.62mm ammo fits nicely into .308 chambers, as a rule.” You CAN encounter problems going the other way, however. A commercial .308 Win round can exceed the max rated pressure for the 7.62×51. So, you should avoid putting full-power .308 Win rounds into military surplus rifles that have been designed for 50,000 psi max. For more information on this interesting topic, read the following articles: Gun Zone’s 30 Caliber FAQ; Cruffler.com Technical Trivia, June 2001; and last, but not least, Steve Redgwell’s .308 vs 7.62×51 Analysis, which really provides a definitive explanation. Reloaders should also note that military ammo often is made with a thicker web. Consequently the case capacity of 7.62×51 brass is usually less than that of commercial .308 brass. You may need to reduce recommended .308 Winchester loads by as much as 2 full grains, if you reload with military 7.62×51 brass, such as Lake City or IMI.
M118 LR and the MilSurp Ammo Option
One reason the .308 Win is so popular is the availability of very inexpensive 7.62×51 military surplus ammo. As explained in more detail above, a 7.62×51 chamber is NOT the same as a SAMMI-spec .308 Win chamber. Nonetheless it is normally safe to shoot 7.62×51 NATO-class ammo in your .308 Win because current .308 Winchester rifles are designed for higher maximum pressures.