We present two ways of analyzing the polarization mode dispersion with random coupling in standard single-mode fibers. The first one is based on the concept of principal polarization states and is valid for highly coherent propagating light (analysis in the frequency domain). The second one is based on unpolarized short pulses split by the local birefringence (analysis in the time domain). The two approaches lead to different definitions of polarization mode dispersion, but we prove that the two definitions lead to the same values. For this purpose we derive the evolution equations for the principal states and for the pulse distribution for arbitrary concatenations of polarization maintaining fibers. Both models have a continuous limit.