By lengthening the strides, shortening the fraction of the cycle that feet are on the ground, and changing the foot fall patterns, horses can move faster than they do at a walk. Pacers and trotters move at rather similar speeds, and these gaits have an interesting similarity to them. The gallop is the fastest of all, running is simply an extended gallop. Compare how many feet are on the ground at any one moment during these strides, and during walking. The turtle, moving more slowly and having its legs placed out to the side of the body needs the more support provided by always having 3 of its feet on the ground.
Tripods are fairly stable configurations.
Horses don't need to worry about stability so much because their legs are under them, more directly beneath the center of gravity. This is just where you'd like legs to be if you want to balance upon them. Thus for example, in the pace or rack not only forward momentum but also limb placement helps keep the horse from falling to one side when both of its feet on that side are in the air. In the ba-bump rythm of the gallop many novel biomechanical tricks are brought into play that facililate locomotion, and that are simply available to the turtle or newt. By switching to a new gait, the skip, kids take advantage of elastic energy stored in their tendons and ligaments which serve as springs.