Colloidal semiconductor nanocrystals (NCs) emitting simultaneously at two distinct wavelengths are of great interest for multiple applications ranging from ultrasensitive self-calibrating nanoscale sensing to light-emitting diodes and white-light emission. The physical mechanism governing dual emission in core/shell NCs composed of two materials is still under investigation; in particular, the roles of the volume of the shell and of the core/shell interface are not well understood. Here we compare three different PbS/CdS NCs with identical cores, but shells of different thicknesses and different core/shell interfaces. We study photoluminescence (PL) characteristics and ultrafast exciton dynamics with subpicosecond time resolution. We find that dual emission is possible for both thick and thin quantum-confined shells, and for different core/shell interfaces. We show that very thick shells allow the decoupling of shell excitons from core ones and we fully describe the dynamic exciton barrier, connected to efficient shell PL. We discuss the efficiency of shell PL in relation to the properties of the NCs and show that it can give rise to optical gain. Our results provide a comprehensive understanding of the physical phenomena governing dual-emission mechanisms in NCs.