Ponies are usually classified as equines that are shorter than 14.2 hands. However, some pony breeds may occasionally have individuals who are over 14.2 hands, but retain all the other characteristics of their breed. There are also some breeds that frequently have individuals who are over 14.2 hands due to modern nutrition and management, but they still keep the historical classification of "pony."
Conversely, the term "pony" is occasionally used to describe horses of normal height. Horses that are used for playing the game of polo are referred to as "polo ponies", even though they are usually of Thoroughbred breeding and often well over 14.2 hands. The term "pony" is sometimes used to describe a full-sized horse in a humorous or an affectionate sense. This is true in American Indian tribes that had a tradition of referring to their horses as "ponies" when speaking English, even though many of the Mustang horses they rode in the 19th century were close to or over 14.2 hands. Today, horses of full height that are owned by Native peoples are still traditionally and affectionately referred to as ponies.
To add further to the confusion, if the preference of a given breed registry is to classify their breed as a "pony," then that is what it will be known as, even if some individuals have horse characteristics. And, of course, some breeds that appear to be pony breeds are called horses simply because the languages of the countries of their origin had only one word for equine and that word translated into English simply as "horse".
But size isn't what makes a pony.
A pony is not simply a small horse. There are horse-sized ponies, and there pony-sized horses, For example, the Miniature Horse, at 8 hands 2 inches high, is a horse, yet the Welsh Pony has many individuals over 14.2 hands, but is still a pony. But being a pony has absolutely nothing to do with size.
So what DOES it have to do with?
Well, the difference between a horse and pony is not simply one of height, but also one of phenotype or appearance. There are noticeable differences in their conformation. Ponies often have thicker manes, thicker tails and a thicker overall coat. They have proportionally shorter legs that give them a lower center of gravity for better surefootedness. And they also have wider barrels, heavier boning, small heads with broad foreheads, and shorter, thicker necks.
Ponies are believed to have originated from the wild horses that developed a small stature due to living on the edges of livable horse territory and needing to survive on what little food was available to them. The ability of taking care of themselves under harsh conditions has led most pony breeds to have a longevity of over 30 years. These smaller animals were eventually domesticated and bred for various purposes all over the world.
Historically, ponies have been used for driving carts carrying people or cargo, as well as a child's first horse. Larger ponies can be ridden by adults, such as the Welsh ponies that were ridden by 15th century knights. And they have been used as "pit ponies," hauling loads of coal up from the mines during the Industrial Age. They are also competitors and performers, too.
But that isn't what makes a pony.
There are noticeable differences in temperament. They often have calmer temperaments than horses and also a high level of equine intelligence that may or may not be used to cooperate with human handlers, which sometimes gets them described as stubborn or devious.
But that STILL isn't what makes a pony.
Even though horses and ponies may look different, both in size and basic body structure; and even though they have what appears to be a different temperament in a generalized sense; all pony breeds and all horse breeds are members of the same genus, species and subspecies for the domestic horse. According to scientific classification, they are Equus caballus caballus. However, this designation can be further broken down into the group classification of Equus caballus caballus pony, which in scientific nomenclature actually refers to an unspecified breed. But when you have to divide the taxonomy of a species' classification all the way down to the group level, there really isn't that much difference between any of the members of the species at all.
So, basically, it is what we can't see, the genetics, that tells them apart -- not the size, not the structure, and not the temperament. Which means that every pony is indeed a horse, but not every horse, even a pony-sized one, is a pony.
And currently, there is debate over whether the feral Chincoteague ponies of Assateague Island are horses or ponies. Perhaps genetics will give the answer.