A pony is most commonly a certain breed of small horse, generally of northern European origin, that usually measures less than 14.2 hh (hands high) at the withers.
The term "pony" can be used in general(or affectionately) for any small horse, regardless of its actual measurements, or breed.
However, some equine breeds are not considered ponies, even if they are under 14.2 hh.
One such breed is the Egyptian Arabian.
Although they are often taller than 14.2 hh, they can sometimes be shorter, but are not considered a true "pony" breed.
The Icelandic Horse and Fjord Horse can also be pony-sized, and of northern European breeding, but they are generally considered horses.
The small horses used for polo are called "polo ponies", though they can be a mixture of both "horse" and "pony" breeds.