I present the recently proposed offset degeneracy, which was shown to unify the close-wide degeneracy for central caustics, and the inner-outer degeneracy for planetary caustics. The offset degeneracy states that for two-fold degenerate lens configurations with any combination of the close, wide, and resonant caustic topologies, the same principle that the source shall pass equidistance to the planetary caustics applies. This shows that the widely cited \(s\leftrightarrow 1/s\) correspondence of the close-wide degeneracy never strictly applies to observed events, and should be more properly referred to as the central caustic degeneracy. I show how the offset degeneracy formalism can be derived directly from the two-body lens equation, which demonstrates its nature as a mathematical degeneracy. I also introduce the pure-shear approximation to planetary microlensing, where a variable-shear Chang-Refsdal lens is shown to approximate the full source-plane behavior for planetary lenses under any caustic topology. It not only demonstrates how the offset degeneracy may be interpreted as a direct generalization of the inner-outer degeneracy, but also allows for approximate analytic and exact semi-analytic magnification solutions that may substantially increase the efficiency of microlensing modeling codes.