  We obtain a unified theory of discrete minimal surfaces based on discrete
holomorphic quadratic differentials via a Weierstrass representation. Our
discrete holomorphic quadratic differential are invariant under M\"{o}bius
transformations. They can be obtained from discrete harmonic functions in the
sense of the cotangent Laplacian and Schramm's orthogonal circle patterns.
  We show that the corresponding discrete minimal surfaces unify the earlier
notions of discrete minimal surfaces: circular minimal surfaces via the
integrable systems approach and conical minimal surfaces via the curvature
approach. In fact they form conjugate pairs of minimal surfaces.
  Furthermore, discrete holomorphic quadratic differentials obtained from
discrete integrable systems yield discrete minimal surfaces which are critical
points of the total area.
