Now I'm curious.
7.62x51 NATO and .308 Winchester brass and ammunition are identical in terms of physical size. (Military - 7.62 - chambers are typically cut a little 'larger' to allow functioning in dirty conditions.)
The only real difference is in loading data, 7.62 gas operated guns have a specific pressure curve to operate the action without damaging the mechanism. (It's a fairly broad curve, but normally requires bullets of less than 175 grains and fast to moderate speed powders.)
The only reason for different sizing dies might be 7.62 brass fired in some military weapons could be 'oversize' and require a slightly wider opening to allow brass to be resized. Also, some die manufacturers have made a 'small base die' to fully resize the base and web area to insure positive chambering in semiautomatic weapons.
Anyone from Dillon want to comment?