Yes, 4WD and 4x4 are the same. It describes the vehicle's capability to go on all 4 wheel drive. But I beg to disagree with some comments here that says AWD and 4WD and 4x4 are just the same, just with different names.

AWD vehicles are either full time 4WD or part time 4WD, part time meaning the ECU commands when to activate the other 2 wheels, depending on the road condition as dictated by different sensors. Most of these AWD are cars and small CUVs, not designed or engineered for off-road driving. In this case, the driver has no control over the 4 wheel drive function. While in the case of 4WD or 4x4, there is a switch or lever to control the activation of 4WD function and gives the driver a choice of 4H, 4L or 2H.

So while 4WD and 4x4 are the same, AWD is different.