There exist two different kinds of farriery in the United States, long footed and short footed; in a similar division, there exist two basic uses of horses, saddle and harness.
    Long footed farriery deals with those horses shod primarily to meet some contrived, artificial standard of what humans have determined subjectively to be desirable motion; obviously, the motion of long footed horses is not related to efficiency.  This class of horses is shod by various methods which are used to enhance or exaggerate the horse's motion and these methods are loosely based on the principle of motion following weight and length of toe.  When shown, American Saddlebreds, National Show Horses, Morgans, Tennessee Walking Horses, Racking Horses, Hackneys, and Arabians can all be considered long footed horses because they are shown with an unnatural length of foot (which may be in the form of natural growth or pads) and/or shoes of a weight in excess of that which would be necessary to protect the foot from environmental hazards.  Other than by definition, neither long footed farriery nor that farriery which applies specifically to harness horses will be considered in this essay.
    Short footed horses are shod for efficiency, although subjectivity (i.e., aesthetic qualities of particular attributes of gait) can often become a primary consideration.  Most often, the foot is trimmed as short as possible while still maintaining the protective attributes of the associated structures.  A short foot is desirable from the standpoint of efficiency because it represents a lever that the horse uses in the transformation of muscle energy into body motion.  Simply put, the shorter the lever, the less work is necessary for a horse to get from here to there.
    Before one can evaluate farriery, one must know a little about the five phases of motion at any gait. How a farrier trims a horse, what type of shoe and the placement of that shoe on the horse's foot can greatly affect the ability of the horse to efficiently perform the necessary transitions of movement within the phases and interphases of motion. The five phases are:

    1.    Support, impact.

    2.    Support, fetlock descending.

    3.    Support, fetlock ascending (transition usually when the
           shoulder passes over the foot). Unloading begins.

    4.    Unloading completed, turnover.

    5.    Unloaded, extension.

    Armed with some basic knowledge of the phases of motion, it becomes evident that an overlong foot and/or too low an angle can cause the foot to remain on the ground longer than efficiency would dictate in the third phase of motion, or that too high an angulation can cause the the transition to take place prematurely.  It's also useful to know that the "head bob" associated with front end lameness (or, "hip hike" in hinds) is the horse's attempt to prematurely unload the affected limb which disrupts the normal transitions between phases.
    It now becomes obvious that unless the horse's feet are trimmed and/or shod in pairs - fronts and hinds - there will be some difference evident in the movement of the horse and that difference will have some effect on efficiency of movement because each foot must complete the five phases of  movement at any gait.  Therefore, unless there's some extremely compelling reason which dictates otherwise, a pair should always have the same effective length of toe and be on the same angle when viewed from the side.  "Effective" because the placement of the shoe can be manipulated in such a manner that the shoe, not the hoof capsule, determines the motion of the foot.
    Assuming proper trimming, the old adage that goes, "Fit the shoe to the foot, not the foot to the shoe", is only half right.  Better said, it would go, "Fit the shoe to the way the foot should be, not the way it is."  The shoe should be fitted in such a way that the entire column of bones which comprise the legs is considered, not just the hoof capsule; it should be a useful extension of that column, not merely an accouterment of the hoof capsule.
    Efficient motion is the most important consideration in shoeing speed horses and/or those horses involved in rapid transitions of movement, especially those transitions involving lateral motion.  This group, in which efficiency of motion is the prime consideration, includes flat racers, barrel horses, jumpers, cutters, reiners, rodeo horses, polo horses, field hunters, using horses, trail horses, endurance horses and most back yard horses.
    At the other end of the scale are those horses that are subjectively judged on the appearance of their stance and/or motion, not the effect that stance and/or motion has on their efficiency.  This group includes dressage horses, hunters, halter horses and virtually all horses shown in rail classes.  These horses are often more difficult to shoe than those shod for efficiency because the element of subjectivity dictates that the farrier must evaluate each individual, then apply whatever methodology best enables the individual to utilize its talent to the maximum level - all within the parameters dictated by a particular discipline.  Obviously, no horse can be made to move any better than it can through farriery, but the difference between red and blue is often a skillful farrier because a skillful farrier will have his horses moving as well as they can.
   Anyone attempting to understand the basics of farriery must first understand that farriers can't "correct" anything.  When confronted by a conformationally challenged individual, a farrier can only apply the correct method of farriery, applicable a given situation, within the allowable parameters of a particular discipline.  This is called, "Giving the horse what it needs", and is primary objective of any form of farriery; thus, "corrective" farriery does not exist.  There is only correct or incorrect farriery:  either the horse gets what it needs or it doesn't.