Dynamics of two distinct bands present in the photoluminescence spectra of non-polar m-plane InGaN/GaN multiple quantum wells (MQWs) was studied by using photoluminescence (PL), cathodoluminescence (CL) and differential transmission (DT) spectroscopy. The competition between these bands caused the large shift of peak emission wavelength with increasing excitation. DT measurements allowed attributing the high-energy PL band to the optical transitions between the ground QW states, while the low-energy PL band was assigned to the recombination of localized carriers. CL measurements confirmed the wide spot-to-spot dispersion of deep localized states and suggested that this disorder occurs on a small spatial scale. PL measurements showed that the distribution of localized states is very sensitive both to indium content and to structure parameters. Temperature-dependent PL studies revealed strong carrier-phonon interaction.