The term 'gaits between walks and canters' refers to the three intermediate gaits of a horse, which are the trot, the pace, and the amble. The trot is a two-beat gait in which the horse moves its legs in diagonal pairs, with the front and hind legs on one side moving together. The pace is a two-beat lateral gait in which the horse moves its legs on the same side together. The amble is a four-beat gait in which the horse moves its legs in diagonal pairs, but with the hind leg leading the front leg on the same side. All three gaits are slower than the canter, but faster than the walk.