Here are the seven most common types of horses and the breeds of horses that correspond with each type.
So all ponies are equines that are shorter than 14.2 hands, but not all equines shorter than 14.2 hands are ponies.
Gaited horses are the product of selective breeding; a.k.a. human interference with a purpose. They were developed by breeding only certain horses that had natural "gaited" abilities.
The term “hot-blooded” is more informal than scientific and describes different breeds with an energetic temperament and more high strung attributes.
These horses were bred for heavy workloads and for agriculture. You will always find a draft horse to be large, both in height and in heft.