They have the same diameter bullet, but the .308 has a bigger case, and thus more gunpowder behind the bullet, which makes for far more muzzle energy for the .308. This translates into much more range for the .308
The AK is designed for close-range firefights, and to be operable by barely-trained peasants.
The NATO .308 rifles are designed to enable a well-trained soldier to get hits out to 800 yards and beyond.