We investigate how accurate different methods of the spectral line shape analysis work in two-dimensional correlation spectroscopy (2D CS) for systems with non-gaussian dynamics. A direct link is established between the frequency dependent correlation functions and a number of line shape metrics. Two model systems are constructed mimicking a typical molecular system with conventional gaussian and non-gaussian spectral dynamics. The frequency dependent correlation function and several line shape parameters extracted from the 2D CS spectra at different waiting times reveal dissimilar dynamics in different frequency domains in the non-gaussian case and similar dynamics in all domains in the gaussian case. The extracted frequency dependent correlation times agree well with the local dynamics in the underlying model for all analysis methods. We also find an extension of the existing line shape analysis methods that allows the extraction of the third-order correlation function.