Equitation classes are judged on the rider, while Hunter classes are judged on the horse. This is true for both flat classes (often called the 'hack' for hunters) and over fences classes. In an Equitation class, the rider should demonstrate their ability to ride effectively, while maintaining a correct position. This isn't a class where rough-and-ready will win - you need to be effective AND pretty. In equitation classes, riders often ride the horses in more contact and may canter in a full seat. Top equitation horses are often a little more "dressage-y". In Hunter classes, the horse is judged, and the judge is looking at the horse's manners, movement and soundness. An ideal hunter is a horse that looks like he is easy to ride (even though the best hunters are often quite quirky and hard to ride!), with big, free gaits that cover the ground efficiently. A horse with little knee action, who carries himself in a relaxed frame on light contact, is a nice hunter type. Hunter riders typically show the horse on a very light contact and show the canter in a halfseat. The rider is not judged in this class, so as long as the rider is not causing the horse to perform badly, their personal style does not matter.
Of course, neither Hunter nor Equitation classes exist in a vacuum, so a good rider is able to get a better performance out of a horse and improve it's placing in a hunter, while a fabulous equitation horse is able to help his rider look better and improve her placing in an equitation class.
ETA: This refers to USEF-style hunter and equitation classes. Breed shows vary a little bit in what they ask of a rider in the equitation classes, from what I've seen. At a USEF rated show, equitation riders may be asked to perform a 'test' on the flat, as a tie-breaker, but the rider will not be asked to complete a "pattern" as a matter of course for the class. Tests are more commonly seen over fences, for the top four riders in a medal class. I've never seen a judge give a flat test in a regular equitation class, although they are allowed to should they chose to do so.
Last edited by KWPNowner; 07-03-2013 at 10:26 AM.