The turn on the forehand is the simplest of the exercises, asking the horse to move his hindquarters around his forehand, so that the hindquarters inscribe an arc. The turn on the haunches asks the horse to move his forehand around the hindquarters, so that the forelegs inscribe an arc, with the horse bent in the direction of the turn.
The simplest movement is the forward swing on the forehand, where the horse moves its hindquarters in a circle around its front legs. In contrast, the turn on the haunches requires the horse to pivot its front legs around its hindquarters, creating a circular motion with the front legs while bending in the direction of the turn.