The pow is a feeling of surfing on snow. You can pow on any mountain after a snowfall or on any virgin terrain. The boards are often softer, with a rocker and a long nose to have a feeling of surf and fun. Pow boards are always a second board.
Freeriding is riding big mountains: Alaska, Whistler, back country expedition. These are more extreme pow conditions where the rider must be educated and careful. The boards are stiffer, a big directional to properly raise the front of the board and they are often more upscale. Mostly, a freeride board is a second board.
All mountain freeride is a day in the mountains but focused on powder. Virgin slopes, glades and powder snow. Boards that are not too soft, with a longer nose in case of heavy snow. This is the type of board that can touch all terrains but should be avoided in a snowpark.
The all mountain freestyle, the name says it all: it's an all mountain board with a good freestyle personality. It's a twin or twin directional board, with both sides equal (or almost) which allows you to walk all over the mountain and finish your run in the park. It's a very versatile all mountain board for the rider who wants to have a single board for all types of day.
The super park is what you see on TV when you watch the X-Games or the Olympics. These are boards made to land jumps of 60 feet and more, to do 2 in 2 out on a down rail, in short, a big park snowboard. The boards are stiffer and often have a pronounced camber, all to better grip the landing of a big jump.
Park boards are made for those who spend their day in the snowpark. They generally have a medium flex with a flat or rocker shape for more fluidity in the snowpark. The person using this board does reasonable size jumps and rails.
The jib is snowpark, but without the jumps. It's all about focusing on the rails, whether that's in your local mountain snowpark or on the streets. A jib board is often softer and rocker for more smoothness on rails and forgiveness on landing. The boards have more resistant bases in order to resist the shocks on the steel of the rails.