Despite significant progress in resonant inelastic x-ray scattering (RIXS) experiments on cuprates at the Cu L -edge, a theoretical understanding of the cross section remains incomplete in terms of elementary excitations and the connection to both charge and spin structure factors. Here, we use state-of-the-art, unbiased numerical calculations to study the low-energy excitations probed by RIXS in the Hubbard model, relevant to the cuprates. The results highlight the importance of scattering geometry, in particular, both the incident and scattered x-ray photon polarization, and they demonstrate that on a qualitative level the RIXS spectral shape in the cross-polarized channel approximates that of the spin dynamical structure factor. However, in the parallel-polarized channel, the complexity of the RIXS process beyond a simple two-particle response complicates the analysis and demonstrates that approximations and expansions that attempt to relate RIXS to less complex correlation functions cannot reproduce the full diversity of RIXS spectral features.