The difference between 4×4 and 4×2 is relating to how many wheels are providing ‘drive’. It means that you either have 2 wheels on one axle giving drive, or, that you have 4 wheels giving you drive, using two axles. It also means that for 4×4 you are using two differentials and 2×4 uses just the one.
More simply put, most standard cars use one differential on a single axle to transfer the drive from the engine to the road via a wheel on each end of that axle. This is 4×2 as the other wheels on the vehicle simply freewheel, transferring no drive at all.
A 4×4 transfers drive from the engine to the road using two differentials, one on each axle, again with a wheel at the end of each axle. Normally there is a transfer box sitting in the middle of this arrangement and this is driven from the gearbox.
Quite a few 4×4 vehicles actually have options to choose either 2×4 or 4×4 dependant on driving conditions and driver requirement. The main reason for having this option is one of fuel economy. Simply put, 2×4 uses less fuel than 4×4. In addition, there is less wear on all moving parts if one is driving in 2×4 as one differential plays no part in the journey. Also, if the drive is put to the front axle, quite a bit of wear can be experienced (over time) as this is a much more complicated set up, as steering has to be accommodated too, so you have CV joints and additional bearings incorporated into the front axle.
One real benefit is that some vehicles such as the Mitsubishi Pajero (Shogun/Monterro) or Suzuki Vitara can be switched from 2 wheel drive to 4 wheel drive while on the move. This means you can take advantage of the fuel economy benefits while driving normally on the road, but, can at any time, switch to 4 wheel drive should road conditions demand it. The Mitsubishi range of vehicles can be switched in such a manner at speeds up to 55 miles per hour, and once switched, one can drive the vehicle at any speed one chooses (speed limits in relative Countries apply). This really does give the driver a big safety factor should one suddenly encounter flooded roads, snow storms and the like.
Other vehicles have permanant 4 wheel drive, which means they have two differentials, one on each axle, providing drive to all wheels all the time. There is of course a cost to this, reflected in fuel economy, but with modern engines this is somewhat countered by the greater efficiencies built into design technology.