We investigate the spectral properties of violet 405 nm (Al,In)GaN laser diodes (LDs). Depending on the substrate the LDs are grown on, the lasing spectra show significant differences. LDs grown on low dislocation GaN substrate have a broad spectrum with several longitudinal modes, while LDs grown on SiC substrate are lasing on a single longitudinal mode.With increasing current, the laser emission of LDs grown on SiC substrate jumps from one longitudinal mode to another (mode hopping), whereas GaN substrate LDs show a smooth but asymmetric mode comb. The different envelopes of these spectra can be understood by assuming a variation of the gain for each individual longitudinal mode. With a high spectral resolution setup, we measure the gain of each longitudinal mode, employing the Hakki-Paoli method. Measurements show a slightly fluctuating gain for the modes of GaN substrate LDs, but much larger fluctuations for LDs on SiC substrate. We carry out simulations of the longitudinal mode spectrum of (Al,In)GaN laser diodes using a rate equation model with nonlinear gain (self saturation, symmetric and asymmetric cross saturation) and including gain fluctuations. With a set of parameters which is largely identical for LDs on either substrate, the simulated spectra truly resemble those typical for LDs on GaN or SiC substrate.