Parameter identification with the pseudo-two-dimensional (p2D) model has been an important research topic in battery engineering because some of the physicochemical parameters used in the model can be measured, while some can only be estimated or calculated based on the measurement data. Various methods, either in the time domain or frequency domain, have been proposed to identify the parameters of the p2D model. While the methods in each domain bring their advantages and disadvantages, a comprehensive comparison regarding parameter identifiability and accuracy is still missing. In this present work, some selected physicochemical parameters of the p2D model are identified in four different cases and with different methods, either only in the time domain or with a combined model. Which parameters are identified in the frequency domain is decided by a comprehensive analysis of the analytical expression for the DRT spectrum. Finally, the parameter identifiability results are analyzed and the validation results with two highly dynamic load profiles are shown and compared. The results indicate that the model with ohmic resistance and the combined method achieves the best performance and the average voltage error is at the level of 12 mV.