  A significant fraction of microlensing planets have been discovered in
high-magnification events, and a significant fraction of these events exhibit a
double-peak structure at their peak. However, very wide or very close binaries
can also produce double-peaked high-magnification events, with the same gross
properties as those produced by planets. Traditionally, distinguishing between
these two interpretations has relied upon detailed modeling, which is both
time-consuming and generally does not provide insight into the observable
properties that allow discrimination between these two classes of models. We
study the morphologies of these two classes of double-peaked high-magnification
events, and identify a simple diagnostic that can be used to immediately
distinguish between perturbations caused by planetary and binary companions,
without detailed modeling. This diagnostic is based on the difference in the
shape of the intra-peak region of the light curves. The shape is smooth and
concave for binary lensing, while it tends to be either boxy or convex for
planetary lensing. In planetary lensing this intra-peak morphology is due to
the small, weak cusp of the planetary central caustic located between the two
stronger cusps. We apply this diagnostic to five observed double-peaked
high-magnification events to infer their underlying nature. A corollary of our
study is that good coverage of the intra-peak region of double-peaked
high-magnification events is likely to be important for their unique
interpretation.
