We study the relationship between the circular polarization of photoluminescence and the magnetic-field-induced spin polarization of the recombining charge carriers in bulk Si and Ge/Si quantum dots. First, we quantitatively compare experimental results on the degree of circular polarization of photons resulting from phonon-assisted radiative transitions in intrinsic and doped bulk Si with calculations which we adapt from recently predicted spin-dependent phonon-assisted transition probabilities in Si. The excellent agreement of our experiments and calculations quantitatively verifies these spin-dependent transition probabilities and extends their validity to weak magnetic fields. Such magnetic fields can induce a luminescence polarization of up to 3%/T. We then investigate phononless transitions in Ge/Si quantum dots as well as in degenerately doped Si. Our experiments systematically show that the sign of the degree of circular polarization of luminescence resulting from phononless transitions is opposite to the one associated with phonon-assisted transitions in Si and with phononless transitions in direct-band-gap semiconductors. This observation implies qualitatively different spin-dependent selection rules for phononless transitions, which seem to be related to the confined character of the electron wave function.