I'm just wondering what the differences are between all-wheel drive, four wheel drive, 4x4 and any other variations there are out there, if there are any differences at all.
4WD and 4x4 are the same thing. Usually meaning a system where under normal driving conditions, the vehicle operates in two wheel drive. When activated (can be automatic or manual activation), a transfer case directs power to the front and rear wheels. The front and rear wheels spin at exactly the same speed, which means driving like this on dry pavement can damage the drive train (when cornering, the front wheels will spin faster than the rear, because the fronts are turning in a larger radius).
AWD is a system where all four wheels are driven all the time. The front and rear axles are usually connected with a viscous coupling, allowing slight differences in wheel speeds between the axles, making it safe for dry pavement operation. This coupling, however, often means poorer performance in demanding off-road situations when compared to a 4x4/4WD system.
There are also 2 divisions in the 4WD (or 4x4) group too. There's part time 4WD and full time 4WD. What Jared described above is part time. Full time 4WD uses a third differential that makes pavement driving possible. Unfortunately, this third differential makes off-road driving impossible because all torque will be tranfered to any wheel that slips. So full time 4WD vehicles will use a locking differential that is engaged for off-road driving.