4X2 is just a 2 wheel drive vehicle, 4X4 has a Transfer-case that when enguaged puts power to the front tires making it 4 wheel drive, with the option of 4 Low. I'm not exactly sure of the physic's of how 4 low works but thats the off-road advantage that AWD (All Wheel drive) does not have.
If you are only taking small trails or it's a road car AWD is great, for real 4 wheeling you want full 4x4.