Why the variety of joints? The variety of situation each joint can be used, and which is the best for your specific situation.
End miter joints, in its most basic form, are formed by mitering the ends of two boards at a 45º angle, then butting the ends together. The disadvantage of this joint is that the glue is entirely on end grain (the weakest glue bond) and there is no form of interlocking between the boards. Basic miter joints are also notoriously difficult to clamp effectively, since the boards will always have a tendency to shift against one-another.
Primarily constructed with the aid of a router, lock joints are variations on dado-and-rabbet joints. Their primary use is to attach drawer fronts to sides, or in locations where one face of a case must resist being pulled away. Regardless of the construction technique, precision cuts are required to ensure this joint mates correctly, but if done correctly it offers significant strength.
Multiple-spline joints are created by cutting slots in both pieces then gluing the joint together with separate splines inserted in the slots. Where the mortise-and-loose-tenon joint has a floating tenon that is oriented from edge to edge of the board, the multiple-spline joint has splines oriented from face-to-face, giving the appearance of box joints.
Multiple-tenon joints for case construction are primarily used for center supports, and seldom, if ever, for the edge of the case. Because of this, the joint has two primary functions: to support the load that might be placed on the board, and to lock the board in place to prevent it from moving. At first look, a multiple-tenon joints resemble blind stopped dado joints, however the multiple-tenons offer some advantages.
Box joints are the "poor man's dovetail joint". It has relatively good mechanical strength, but does not have the interlocking capabilities given by the sloping of the dovetail pins and tails. The box joint does still provide an incredible amount of gluing surface, making it a strong joint.
Butt joints are one of the weakest forms of case joints, but they are the easiest and quickest to make. A butt joint is achieved whenever you join the straight and square end grain of one board to face grain of another board. End grain is notoriously difficult to glue or fasten, and butt-joints present the smallest amount of surface area to be used for gluing. In order to achieve any significant strength and sturdiness, you must reinforce the joint.
Corner block joints are intermediaries. Instead of connecting two boards directly together, each board is connected to the corner block instead.
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