ABSTRACT We examine the 1.4 GHz radio luminosities of galaxies arising from star formation and active galactic nuclei (AGNs) within the state-of-the-art cosmological hydrodynamic simulation Simba. Simba grows black holes via gravitational torque limited accretion from cold gas and Bondi accretion from hot gas, and employs AGN feedback including jets at low Eddington ratios. We define a population of radio loud AGNs (RLAGNs) based on the presence of ongoing jet feedback. Within RLAGN, we define high and low excitation radio galaxies (HERGs and LERGs) based on their dominant mode of black hole accretion: torque limited accretion representing feeding from a cold disc, or Bondi representing advection-dominated accretion from a hot medium. Simba predicts good agreement with the observed radio luminosity function (RLF) and its evolution, overall as well as separately for HERGs and LERGs. Quiescent galaxies with AGN-dominated radio flux dominate the RLF at $\gtrsim 10^{22-23}$ W Hz−1, while star formation dominates at lower radio powers. Overall, RLAGNs have higher black hole accretion rates and lower star formation rates than non-RLAGN at a given stellar mass or velocity dispersion, but have similar black hole masses. Simba predicts an LERG number density of 8.53 Mpc−3, ∼10× higher than for HERGs, broadly as observed. While LERGs dominate among most massive galaxies with the largest black holes and HERGs dominate at high specific star formation rates, they otherwise largely populate similar-sized dark matter haloes and have similar host galaxy properties. Simba thus predicts that deeper radio surveys will reveal an increasing overlap between the host galaxy demographics of HERGs and LERGs.