The soft-gaited horse moves in a unique fashion that produces a definite four beat rhythm when it moves into its "second gear." This is natural to the soft-gaited breeds. Their ability to move in this special fashion is a part of their genetic make-up and these gaits for the most part, can't be easily taught to horses designed to trot.
Since most soft-gaited horses have the ability to perform more than one of these specialized gaits, it is important for them to be trained to stick to one at a time. It can be confusing to riders new to the soft-gaited horses. It is easy to become bewildered by the horse's "shifting of gears."
Are there any similarities with walk-trot horses? Yes, all horses have one 4-beat gait in common. It is the walk.
The walk is a gait that all horses perform in the same manner. A walk is four-cornered, with each foot leaving the ground and then hitting the ground independently. The horse always has two or three feet on the ground at once. There is alternation between two front and one rear and two rear and one front. Each foot is off the ground for the same even interval of time. This is what produces a smooth, even comfortable gait.
The difference in smoothness and comfort between the walk and the trot is the same difference in smoothness and comfort between the trot and the running walk, rack, fox trot, paso fino, tolt, saddle gait and the rest of the soft gaits that are peculiar to the soft-gaited breeds.
It's in the genes! :o)