Domestic horses and ponies are the same species with different breeds.
Horses are generally defined as over 14.2 hands and ponies at under 14.2 (a "hand" is 4 inches, measured to the horse's withers - shoulder top;
14.2 hands is 14 hands plus 2 inches = 58", nearly 1.5 metres), but this isn't always the case and there are dwarf horses and very large ponies.
Ponies in the UK fall into three main groups: working ponies (farms, mines, etc. not so many as in former years),
companion and private riding animals, and the semi-feral but fully-owned and supervised free-roaming herds, mainly in
National Parks such as the New Forest, Dartmoor, Exmoor, Lakeland Fells and others. All 3 groups are in decline.
Ponies shown in the two rows above are mainly on Dartmoor plus one photo of the New Forest.