One of the things they talked about in the program was the gait of galloping and how horses have raced for many years. When artists first started painting horses in gallop they could not tell what the horse's legs were doing. They thought that the horses had all 4 legs off the floor at the same time (which is true) but they painted them with the legs stretched out. This can be seen on the images below.
Painting from the Epsom Derby 1821 by Theodore Gericault
Painting of a Derby by Anand Swaroop Machiraju
The video below is from YouTube and is a slow motion video of a horse galloping. From this it can be seen that the horse does have all 4 legs off the floor at one time but they are all tucked up underneath it.
The gallop is a four-time pace like the walk as all of the legs are moving at different times. The trot is a two-time pace and the canter is three-time.
(None of the images or videos used in this post belong to me!)