We studied the light emission of crystalline Si nanoparticles (SiNPs) with hydrogen and native oxide shell terminations using temperature- and time-dependent photoluminescence. We demonstrate that the broad emission normally observed for SiNPs after natural oxidation is in fact formed of two components, which originate from distinct recombination mechanisms that take place simultaneously in the same SiNPs sample. To identify the two spectral components, we exploited the different time scales associated with different emission mechanisms by carefully choosing the measurement time window at which only one of the emission mechanisms is active. Moreover, our experiments indicate that one of the emissions is due to recombination of photogenerated electrons and holes located in the crystalline core of the SiNPs (excitonic emission) whereas the other component originates from donor-acceptor recombination pairs involving states associated with the native oxide shell. These conclusions are supported from experiments carried out with the same SiNPs but where the surface-oxide shell is replaced by H termination. We conclude that both emission components are excited through electronic states of the SiNPs core, pointing out an effective core-to-shell energy/charge transfer. Furthermore, we show that the light emission quantum yield of SiNP ensembles is strongly affected by inter-NP charge transfer and therefore is not determined solely by the properties of the individual NPs. High quantum yields of up to 43%, observed for our surface-oxidized SiNP samples in solution, result from inhibition of inter-NP charge transfer.