A hackamore is a type of animal headgear which does not have a bit. Instead, it has a special type of noseband that works on pressure points on the face, nose, and chin. Hackamores are most often seen in western riding and other styles of riding derived from Spanish traditions, and are occasionally seen in some English riding disciplines such as show jumping and the stadium phase of eventing. Various hackamore designs are also popular for endurance riding. While usually used to start young horses, they are often seen on mature horses with dental issues that make bit use painful, and on horses with mouth or tongue injuries that would be aggravated by a bit. Some riders also like to use them in the winter to avoid putting a frozen metal bit into a horse's mouth.
A horse wearing a bosal hackamore with a fiador.
A horse wearing a bosal-style hackamore
5th century AD Eastern Roman mosaic from the emperor's palace in Constantinople.
an English style jumping cavesson
A bridle is a piece of equipment used to direct a horse. As defined in the Oxford English Dictionary, the "bridle" includes both the headstall that holds a bit that goes in the mouth of a horse, and the reins that are attached to the bit. It provides additional control and communication through rein pressure.
A hunt seat style English bridle
Western show bridle
The crownpiece runs over the horse's poll, and the browband across the forehead. The cheekpieces run down the sides of the horse's face.
A double bridle, using two bits