VideoShowCanter (Download versions) VideoTrailCanter
On the black & white trail horse, watch the left rear hoof hit the ground first, then the left front and right rear hit simultaneously, followed by the right front hoof; thus, the 3 beats of a Three Beat Canter. Notice the low easy motion and the way there is almost always weight on the ground, thus giving the rider a smooth ride and allowing the horse to go long distances.
The Canter performed today by most show horses does not have the same 3 beat pattern for which it got its name. The few that do the correct pattern still have followed the show trend of slowing down the gait and pumping the horse so it's front end comes way up in the air, rather than gliding along the ground. This is considered by many to be very beautiful. The show canter is also very slow....slower in fact than the foxtrot, whereas the lope (natural canter) is faster than foxtrotting, but slower than a 4 beat gallop or run.
There are several streams of thought about these gaits: The first claims that successfully teaching a horse to do the show gait well proves that horse's trainability & that it is more exciting to watch. Another philosophy is that if a horse is that trainable and well gaited then all that talent and effort should be put into helping it reach its full potential to perform a smoother and more "useful" gait such as the lope, which happens to be the natural "canter" of the foxtrotter. Others claim that you should teach them to do one in the show and the other on the trail. Each to his own, I guess.