Numerical simulations and experiments demonstrate the equivalence of two self-switches based on semiconductor optical amplifiers, namely the nonlinear polarization switch and the Mach-Zehnder interferometer. This equivalence is highlighted by introducing a one-to-one functional similarity among the switch components. By means of a detailed study on gain and phase difference variations in both switches, we introduce a method to determine the configurations in which the switches exhibit an equivalent power transfer function. Their operational equivalence is experimentally confirmed.