Every horse has the gait called a "pace".
pace == smaller more rhythmic bounces (less "flying") Great for harness racing as the smaller movements are good for control. Would beat the Saddle Rider to death, from the Butt-up.
gallop == Larger less rhytmic bounces, more "flying". Great for saddle riding as there is a longer rhythm to it. Would bounce the heck out of the cart for the rider if used for harness racing.