All of this is useful for interpreting the animal's actions and not just for species identification. For instance, the diagonal walking pattern of a coyote indicates a normal walk, but the diagonal walking pattern of a raccoon indicates the animal was in a hurry. While an animal's normal gait is its slow speed, there are times when animals slow down even more. When stalking, for instance, most animals leave a track pattern that looks just like a diagonal walk. However, the movements used to make it are about midway between a diagonal walk and a pace.
Most animals use a slow pace when being antagonistic or when trying to appear threatening.
Pacing makes them look broader and more imposing. Let's use humans as an example. There are more than 30 different recognizable gaits for diagonal walkers, each indicating a particular speed and state of mind. The best way to learn these is to watch the animals and then examine their tracks. But the basics covered above should get you started thinking about the behavior of the animal that left the tracks behind.