Given the multiple energy loss mechanisms of cosmic ray electrons in galaxies, the tightness of the infrared - radio continuum correlation is surprising. We extended the analytical model of galactic disks of Vollmer et al. (2017) by including a simplified prescription for the synchrotron emissivity. The galactic gas disks of local spiral galaxies, low-z starburst galaxies, high-z main sequence starforming, and high-z starburst galaxies are treated as turbulent clumpy accretion disks. The magnetic field strength is determined by the equipartition between the turbulent kinetic and the magnetic energy densities. Our fiducial model, which neither includes galactic winds nor CR electron secondaries, reproduces the observed radio continuum SEDs of most (~70%) of the galaxies. Except for the local spiral galaxies, fast galactic winds can potentially make the conflicting models agree with observations. The observed IR - radio correlations are reproduced by the model within 2 sigma of the joint uncertainty of model and data for all datasets. The model agrees with the observed SFR - radio correlations within ~4 sigma. Energy equipartition between the CR particles and the magnetic field only approximately holds in our models of main sequence starforming galaxies. If a CR electron calorimeter is assumed, the slope of the IR - radio correlation flattens significantly. Inverse Compton (IC) losses are not dominant in the starburst galaxies because in these galaxies not only the gas density but also the turbulent velocity dispersion is higher than in normally starforming galaxies. Equipartition between the turbulent kinetic and magnetic field energy densities then leads to very high magnetic field strengths and very short synchrotron timescales. The exponents of our model SFR - radio correlations at 150 MHz and 1.4 GHz are very close to one.