In this work, we present a detailed analysis of the interplay of Coulomb effects and different mechanisms that can lead to carrier-localization effects in c-plane (In,Ga)N/GaN quantum wells. As mechanisms for carrier localization, we consider here effects introduced by random alloy fluctuations as well as structural inhomogeneities such as well-width fluctuations. Special attention is paid to the impact of the well width on the results. All calculations have been carried out in the framework of atomistic tight-binding theory. Our theoretical investigations show that independent of the well widths studied here, carrier-localization effects due to built-in fields, well-width fluctuations, and random-alloy fluctuations dominate over Coulomb effects in terms of charge-density redistributions. However, the situation is less clear cut when the well-width fluctuations are absent. For a large well width (approximately >2.5nm), charge-density redistributions are possible, but the electronic and optical properties are basically dominated by the out-of-plane carrier separation originating from the electrostatic built-in field. The situation changes for lower well widths (