Most NATO General Purpose Machine Gun (GPMG) rounds today are all 7.62 x 51 mm (generally known in the civilian world as the .308 Winchester. Essentially both the .308 and the .30-06 cartridges use the same bullet (.30-06 can accomadate a slightly heavier bullet, though) but I believe that the .308 cartridge is just a shortened .30-06 casing to reduce the power of the round and reduce its effective engagement range to about a kilometer. The .30-06 cartridge is known in the military as the 7.62 x 63 mm round.
You do have to be careful when you hear the term "30-caliber" used to describe a machine gun round since there are a lot of battlefield cartridges out there that discharge 30-caliber bullets. In general these cartridges can be broken down into three categories of 30-caliber rounds - Pre-Post War US, Post War NATO, and Warsaw Pact. Pre-Post War US .30-cal machine guns, such as the Browning M1919 and the Browning Automatic Rifle (BAR) used the .30-06 cartridge as it was the standard infantry round of the day. Post War NATO machine guns, like the M-60 and M-240 use the .308 round. And Warsaw Pact systems, like the AK-47, RPD, and RPK, are chambered for the Soviet 7.62 x 39 mm M43 cartridge.
For more information on machine guns, check out Modern Firearms, an online Military Firearms encyclopedia.
Enjoy your research!
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