There is definitely a difference....despite some of the opinions above.
The difference is perhaps a moot point in modern rifles with modern chambers, but if you find yourself with a Spanish pre-98 Mauser with "7.62" on the barrel, like my FR-7, you'll be on the Darwin Award's short list if you run modern commercial .308Win loads through it. Not only were they designed for lower pressure (around 40K PSI, vs. 7.62NATO around 50K PSI, and .308 Win around 60K PSI), but also the metallurgy 100 years ago was nowhere near what it is today.
A fellow was killed when his gun blew up not too long ago.
Do a web search on 7.62 CETME & .308 Winchester. they are near-identical cartridges, looking at case dimensions, but the Spanish cartridge came out before NATO was around, and before NATO specs were conceived.
I mean, if they were the same, why would DPMS differentiate between the two? They should know, since they are in the business...
For further proof, use a rifle that can handle .308win (and therefore 7.62NATO) and shoot a couple of rounds of each....they'll feel different, and they'll impact different. That's also a good indicator that they are different.