While gravitational microlensing by planetary systems can provide unique vistas on the properties of exoplanets, observations of such 2-body microlensing events can often be explained with multiple and distinct physical configurations, so-called model degeneracies. An understanding of the intrinsic and exogenous origins of different classes of degeneracy provides a foundation for phenomenological interpretation. Here, leveraging a fast machine-learning based inference framework, we present the discovery of a new regime of degeneracy–the offset degeneracy– which unifies the previously known close-wide and inner-outer degeneracies, generalises to resonant caustics, and upon reanalysis, is ubiquitous in previously published planetary events with 2-fold degenerate solutions. Importantly, our discovery suggests that the commonly reported close-wide degeneracy essentially never arises in actual events and should, instead, be more suitably viewed as a transition point of the offset degeneracy. While previous studies of microlensing degeneracies are largely studies of degenerate caustics, our discovery demonstrates that degenerate caustics do not necessarily result in degenerate events, which for the latter it is more relevant to study magnifications at the location of the source. This discovery fundamentally changes the way in which degeneracies in planetary microlensing events should be interpreted, suggests a deeper symmetry in the mathematics of 2-body lenses than has previously been recognised, and will increasingly manifest itself in data from new generations of microlensing surveys.