Herein, we build on the results of previous works describing the use of advanced photocatalytic processes for effective industrial wastewater treatment and investigate SrZnTiO3/g-C3N4 heterostructure (SZTO/CN)-catalyzed removal of rhodamine B (RhB) and indigo carmine (IC), probing the effects of the light source (UV and visible) on charge transfer (Z-scheme and non-Z-scheme) in the above heterostructure. Both RhB (cationic dye) and IC (anionic dye) could be efficiently removed by SZTO/CN, which also exhibited elevated photocurrent responses. In particular, the efficiencies of IC and RhB removal over a SZTO/CN sample with a CN/(SZTO + CN) mass ratio of 0.8 after 3-h visible-light irradiation equaled 93.1 and 82.2%, respectively, while the respective values for STO were obtained as 9.7 and 21.8%. Dye degradation under UV light irradiation (e.g., within 30 min for IC) was much faster than under visible light irradiation (e.g., within 180 min for IC), and optimal CN/(SZTO + CN) ratios were individually determined for both irradiation types. Notably, the best performing catalyst maintained over 95% of its initial photocatalytic performance after five consecutive IC decomposition runs, and the X-ray diffraction patterns of cycled and non-cycled catalysts indicated that cycling did not induce any notable crystalline structure changes. The reactive species involved in photocatalytic degradation were identified as O-2(center dot-), h(+), and OH center dot for both light source types, which, together with the results of band energy structure analysis and hydroxyl radical population measurements allowed us to propose two light source-dependent photocatalytic dye removal mechanisms. Thus, it was concluded that the developed SZTO/CN heterostructure can be sustainably applied to the treatment of dye-contaminated wastewater.