A detailed study of the excitation dependence of the photoluminescence (PL) from monolayers of MoS2 and WS2/MoS2 heterostructures grown by chemical vapor deposition on Si substrates has revealed that the luminescence from band edge excitons from MoS2 monolayers shows a linear dependence on excitation intensity for both above band gap and resonant excitation conditions. In particular, a band separated by similar to 55 meV from the A exciton, referred to as the C band, shows the same linear dependence on excitation intensity as the band edge excitons. A band similar to the C band has been previously ascribed to a trion, a charged, three-particle exciton. However, in our study the C band does not show the 3/2 power dependence on excitation intensity as would be expected for a three-particle exciton. Further, the PL from the MoS2 monolayer in a bilayer WS2/MoS2 heterostructure, under resonant excitation conditions where only the MoS2 absorbs the laser energy, also revealed a linear dependence on excitation intensity for the C band, confirming that its origin is not due to a trion but instead a bound exciton, presumably of an unintentional impurity or a native point defect such as a sulfur vacancy. The PL from the WS2/MoS2 heterostructure, under resonant excitation conditions also showed additional features which are suggested to arise from the interface states at the heteroboundary. Further studies are required to clearly identify the origin of these features.