I found this a useful description of each of the different boards:
eBay Australia's Snowboard Gear Buying Guide
Freestyle snowboards: An excellent choice for beginners, freestyle snowboards are short, wide, flexible as well as very responsive and forgiving over harsh terrain. Designed for half pipes and terrain parks, most freestyle snowboards are symmetrical and have shovels on both ends. Some are directional-twin, which means that while they have the same shape on both ends, the tail is stiffer than the nose.
Freeride snowboards: Due to its versatility, the freeride snowboard is the most popular out of the three snowboard types and account for almost half of all snowboard sales. Typically directional with the tail thinner than the nose, freeride snowboards bridges the gap between freestyle and alpine carving by combining some aspects of both the alpine snowboards and freestyle snowboards. They are more rigid than freestyle boards, so they’re good for carving long turns, but they are not as rigid as alpine snowboards.
Alpine snowboards: Also known as carving snowboards, apine snowboards are stiff, narrow and straight. Because of this, they almost look like an enlarged ski. Designed for speed, clean curves and sharp turns, they are made in both symmetrical and asymmetrical styles and usually only have a shovel at one end. Due to their stiffness, they are generally reserved for the more advanced riders who are looking for a snowboard built for downhill.