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When a horse is loping or galloping the legs on one side of its body lead, or reach forward farther than the legs on the other side. In a left lead a horse will reach the left hind leg and the left front leg farther forward than the right legs. For a right lead, the opposite is true: The legs on the right side of the horse's body will reach forward farther than the legs on the left side.
It is important to note that leads are unique to the gaits of lope (also called a canter) and gallop. During other gaits (walk, trot, and others) a horse moves its legs differently than it does during a lope or gallop and the concept of leads does not apply.
When a horse is loping or galloping there are times where using one lead or the other will be considered right (as in correct) or wrong. For example, when a horse is loping or galloping in a bend or a circle it will be more athletic when it is using the lead on the inside of the bend or circle. Therefore, in most cases, an "inside" lead will be considered the correct lead and an "outside" lead will be considered incorrect.
So, if a horse is loping or galloping while bending or circling to the left, a left lead will be the inside lead and will usually be considered the correct lead. Conversely, when a horse is loping or galloping while bending or circling to the right, a right lead will be the inside lead and will typically be thought of as the correct lead