The high light-output efficiencies of In(x)Ga(1-x)N quantum-well (QW)-based light-emitting diodes (LEDs) even in presence of a large number of non-radiative recombination centers (such as dislocations) has been explained by localization of carriers in radiative potential traps, the origins of which still remain unclear. To provide insights on the highly efficient radiative traps, spectrally resolved photoluminescence (PL) microscopy has been performed on green-light-emitting In(0.22)Ga(0.78)N QW LEDs, by selectively generating carriers in the alloy layers. PL imaging shows the presence of numerous inhomogeneously distributed low-band-gap traps with diverse radiative intensities. PL spectroscopy of a statistically relevant number of individual traps reveals a clear bimodal distribution in terms of both band-gap energies and radiative recombination efficiencies, indicating the presence of two distinct classes of carrier localization centers within the same QW sample. Disparity in their relative surface coverage and photoemission "blinking" characteristics suggests that the deep traps originate from local compositional fluctuations of indium within the alloy, while the shallow traps arise from nanometer-scale thickness variations of the active layers. This is further supported by Poisson-Schrodinger self-consistent calculations and implies that radiative traps formed due to both local indium content and interface-morphology-related heterogeneities can coexist within the same QW sample.