To me, 4x4 means off-roader (most often with selectable 2/4WD and high/low ratio), 4WD means usually 2WD but with a locking centre differential so when the two usually driven wheels slip and AWD means things like Evos, Imprezas, Skyline GT-Rs, the GT-R, most Lamborghinis; basically all wheels being driven full-time and not just when two have no traction.
I remember once at Santa Pod drag strip, when I was younger, I saw several cars only spinning up one wheel and thought 'why would one-wheel drive be useful at a drag strip?'... Didn't realise what an LSD did.
So my favourite 4x4 in the game is the 80's Pajero Rally Raid Car, I wish I had one but I had more important things to buy on the one occasion it popped into the UCD. Shame.
Edit: I started writing this, went off to do other stuff, then came back, hence why the first paragraph is so redundant now.