The taining aid is to help the rider to work his horse, on foot or mounted. The main objective of these reins is to orient the horse to a low position, which allows to work its back, its amplitude, its muscles etc.
The martingale is a light rein most often used in jumping. It prevents the horse from going over the rider's hand. The horse's shoulders are freed, two rings are attached to the reins.
The Howlett is a relatively soft and educational rein. The rope of the martingale passes through the rings of the bit and is attached to rings along the reins. It allows the rider to have only one pair of reins compared to other ordered reins. This rein makes it easier to tension your horse and to get a better rein tension.
The gullet is a rein that promotes tension, building up the topline by stretching your horse and thus causing the base of the neck to rise.
Fixed gogue: Most often used for lunging work.
Controlled gogue: only for mounted work.
Draws reins have a lowering effect on the horse's neck and nape. They run through the bit and are attached to the girth between the horse's forelegs. It is a removable reinset that is adjusted by the rider's hand in the moment.
The Breastplate is a leather piece that is placed on the horse's forehand. Its purpose is to prevent the saddle from sliding backwards. Most often used in show jumping or cross country, they are fitted with a martingale fork to limit the horse's upward head movement.