The Rayleigh–Fourier and extinction theorem method mathematical formalisms are established and compared in the case of acoustic scattering in a waveguide with impedance boundary conditions and one nonplanar surface. It is shown that the two methods are theoretically equivalent by using the properties of the solution given by the extinction theorem method. This result, which is confirmed by a perturbation approach, may be of practical importance in view of the better computational efficiency of the Rayleigh–Fourier method.