All wheel drive or AWD means that the vehicle is designed to provide power to all four wheels at the same time, and in most cases cannot be switched to the two wheel drive (2WD) option. The distribution of power to the front set and hind set of wheels differs from one system to another. 4WD or four wheel drive (part time and full time) also means the vehicle has a drivetrain that allows all four wheels to receive torque from the engine simultaneously. AWD and full time 4WD essentially mean the same thing except for some difference in the power settings. 4WD has three settings: 2WD (two wheel drive), low and high whereas in case of AWD, the 2WD option is absent. These terms are interchangeably by car manufacturers, so you should ask for detailed information about the vehicle, before investing in one.
In case of vehicles with more than 4 wheels, AWD implies that all the wheels are powered whereas in 4WD means that all four wheels are being powered.
edit Pros and Cons of AWD and 4WD
AWD systems and full time 4WD systems have a central differential that allows it to run on any road conditions and is designed for all season use. However, it consumes more fuel and is more expensive than other systems. Part time 4WD systems, however, have to be engaged from a two wheel to four wheel mode when needed and disengaged when not required to avoid mechanical damage. This can be cumbersome if one is used to travelling in rough conditions. This system is ideal for people who do not want to buy an expensive 4WD and still want the option for occasional use.
edit Types of AWD and 4WD
AWD can be automatic or selectable AWDs. Automatic AWD, as the name suggests is an on-demand system, which means that in normal road conditions only one axle of the vehicle is engaged. In rough road conditions, the second axle becomes engaged. In selectable AWDs, you can choose between degrees of wheel engagement. This type of system in seen in cars or crossover SUVs.
4WDs can be part time or full time 4WDs. Part time 4WDs are designed so that the settings can change from 2WD to low or high 4WD manually using a lever or switch. 2WD condition is used to drive on normal road conditions. Low 4WD settings are use to drive on very slippery roads, sand, steep areas or mud where the speed of the car is very low (generally below 25mph). High settings are used when driving on snow, ice, rocky roads when you can drive at higher speeds.
The 4WD feature, however, has to remain disengaged while driving on a dry pavement. The change in the settings can be done while driving only in the newer models. In older models, the car has to come to a complete halt before changing it to the low setting to avoid mechanical damage. This type of system is advantageous for people who do not intend to use 4WD all the time and only want it for safety on a slippery road.
Fulltime 4WD can remain engaged all the time, even when driving on a dry pavement although there is an option to switch from high to low setting which has to be done when the car is at a halt. This system is generally seen in trucks or heavy SUVs.
Some examples of vehicles with AWD are Pontiac Vibe, Toyota Matrix, Ford Fusion etc. Examples of part time 4Wd are Suzuki SUVs, and fulltime 4WD are Toyota Sequoia, Mitsubishi Montero etc.
edit Video explaining the differences