Is it: The statistical variations inherent due to the discrete nature of the photon? The statistical variations inherent due to the discrete nature of the electron? The randomness caused by the photon to electron conversion process? Or is shot noise due to all 3?
It is the statistical variation due to all three. However, assuming you are collecting data from a photodetector / photodiode, your data corresponds most directly to the flow of electrons and therefore it is the variation in discrete electrons that has the final and most direct influence on the noise in your data.
This application note on shot noise measurements with low noise photodetectors explains shot-noise in more detail and the effect of quantum efficiency.