Photoionization time delays have been studied in many streaking experiments in which an attosecond pulse is used to ionize the atomic or solid state target in the presence of a dressing infrared laser field. Among the methods of extracting the time delay from the streaking spectrogram, the simplest one is to calculate the first moment of the spectrogram and to measure its offset relative to the vector potential of the infrared field. The first moment method has been used in many theoretical simulations and analysis of experimental data, but the meaning of this offset needs to be investigated. We simulate the spectrograms and compare the extracted time delay from the first moment with the input Wigner delay. In this study, we show that the first moment method is valid only when the group delay dispersions corresponding to both the spectral phase of the attosecond pulse and the phase of the single-photon transition dipole matrix element of the target are small. Under such circumstance, the electron wave packet behaves like a classical particle and the extracted time delay can be related to a group delay in the photoionization process. To avoid ambiguity and confusion, we also suggest that the photoionization time delay be replaced by photoionization group delay and the Wigner time delay be replaced by Wigner group delay.