Difference between anaerobic and Aerobic respiration with horse?

Aerobic respiration is a process of cellular respiration that uses the oxygen in order to break down the molecules, which then release electrons and creating energy.

Anaerobic respiration does not need the oxygen. It happens when there is not enough oxygen for aerobic respiration.

Basicly it is the same with horses and humans, and what it means is that for example cross country horses are not galloping at the top speed between the fences because they would not have enough energy after first two or three fences due to lack of oxygen in their bodies. Therefore they use all the energy on jumping over the fences and then they have steady canter to gain the energy they have lost for the next fences.

Hope it gives you the basic idea of what is happening in each of above processes.