AWD is all wheel drive. Usually they are found on cars and fake SUVs. They are no good for offroad use, since they lack low ratios and differential locks. This is there to combat understeer and oversteer, which are relitive to FWD and RWD cars respectively.
4WD on the other hand refers to two seperate gearboxes, and allow for different gear ratios to be selected for each.
This is what is used offroad. As it gives you much more control and traction at low speeds. Ie when you are stuck or something.