The signature of mass-independent fractionation of quadruple sulfur stable isotopes (S-MIF) in Archean rocks, ice cores, and Martian meteorites provides a unique probe of the oxygen and sulfur cycles in the terrestrial and Martian paleoatmospheres. Its mechanistic origin, however, contains some uncertainties. Even for the modern atmosphere, the primary mechanism responsible for the S-MIF observed in nearly all tropospheric sulfates has not been identified. Here we present high-sensitivity measurements of a fifth sulfur isotope, stratospherically produced radiosulfur, along with all four stable sulfur isotopes in the same sulfate aerosols and a suite of chemical species to define sources and mechanisms on a field observational basis. The five-sulfur-isotope and multiple chemical species analysis approach provides strong evidence that S-MIF signatures in tropospheric sulfates are concomitantly affected by two distinct processes: an altitude-dependent positive 33S anomaly, likely linked to stratospheric SO2 photolysis, and a negative 36S anomaly mainly associated with combustion. Our quadruple stable sulfur isotopic measurements in varying coal samples (formed in the Carboniferous, Permian, and Triassic periods) and in SO2 emitted from combustion display normal 33S and 36S, indicating that the observed negative 36S anomalies originate from a previously unknown S-MIF mechanism during combustion (likely recombination reactions) instead of coal itself. The basic chemical physics of S-MIF in both photolytic and thermal reactions and their interplay, which were not explored together in the past, may be another ingredient for providing deeper understanding of the evolution of Earth's atmosphere and life's origin.