This paper discusses the properties of two-dimensional, nonlinear, potential and vortex waves on the surface of an ideal liquid of infinite depth. It is shown that to quadratic order in the amplitude, the vorticity of the Gerstner wave is equal in magnitude and different in sign to that of the Stokes drift current in a surface layer. This allows a classic Stokes wave obtained in the framework of potential theory to be interpreted as a superposition of the Gerstner wave and Stokes drift. It is proposed that the nonlinearity coefficient in the nonlinear Shrödinger equation can be physically interpreted as the Doppler frequency shift over the vertically averaged Stokes drift current.