Some coaches do teach it differently, unfortunately, but I've always associated wall slams with rotational/lateral movement.
Like nighthawkz said. Basically the reverse of an overhead slam. Instead of throwing it down to the ground, it's up overhead. Focus more on throwing "up" instead of "back."
Think 'wall ball with a much more shallow squat and minus the wall.'
I'd go close-ish, and yep, with a twist.
The push press version has a little more leg drive. So, quarter squat down, then stand up and press at the same time.