The inside rein and outside rein serve fundamentally different functions, and understanding those functions — and keeping them appropriately separated — is one of the keys to educated riding in any discipline. Conflating the two functions, or using both reins to do the same thing simultaneously, produces a horse that is blocked, confused, or trained to brace against contact rather than yield to it.
The inside rein asks for flexion — bend of the horse's neck toward the inside of the turn or circle, softness through the jaw and poll, and lateral suppleness through the horse's topline. It invites the horse's nose to the inside. The inside rein should be used with a giving, yielding action — applying pressure to ask for flexion and releasing the moment the horse softens — rather than a holding, pulling action that fixes the horse's head in a bent position.
The outside rein regulates — it controls the degree of bend by limiting how much the inside rein can pull the nose, it maintains the horse's pace by providing resistance to forward falling, and it guides the horse's shoulder to prevent it from falling outward through turns. The outside rein is the primary steering rein in educated riding, with the inside rein asking for suppleness and the outside rein defining the shape of the movement.
The most common mistake riders make is using too much inside rein and too little outside rein — pulling the horse's nose to the inside while the shoulder falls out and the horse swings its haunches instead of bending through its whole body. The correction is almost always to soften and give with the inside rein while maintaining or increasing the outside rein contact, which straightens and regulates the horse and allows true bend rather than just neck bend to develop.