Several mathematical models exist in the literature to describe the properties of optical resonators. Here, coupled mode theory and coherent superposition theory are compared and their consistency is demonstrated as they are applied to phase-shift cavity ring-down measurements in optical (micro-)cavities. In the particular case of a whispering gallery mode in a microsphere cavity these models are applied to transmission measurements and backscattering measurements through the fiber taper that couples light into the microresonator. It is shown that both models produce identical relations when applied to these traveling wave cavities.