Geometrical Shock Dynamics (GSD) is a simplified model for nonlinear shock wave propagation. It is based on the decomposition of the shock front into elementary ray tubes with a simple relation linking its local curvature and velocity. This relation is obtained under the assumption of strong shock in order to neglect the effect of the post-shock flow on the front. More recently, a new simplified model, referenced as the Kinematic model, was proposed. This model is obtained by combining the three-dimensional Euler equations and the Rankine-Hugoniot relations at the front, which leads to an equation for the normal variation of the shock Mach number at the wave front. In the same way as GSD, the Kinematic model is closed by neglecting the post-shock flow effects. Although each model's approach is different, we prove here their structural equivalence: the Kinematic model can be rewritten under the form of GSD with a specific A − M relation. Both models are thus compared through a wide variety of examples including experimental data or Eulerian simulations results when available. Attention is drawn to the simple cases of compression ramps and convex corners' diffraction. The analysis is completed by the more complex cases of the diffraction over a cylinder, a sphere, a mound and a trough.