Given the multiple energy-loss mechanisms of cosmic-ray (CR) electrons in galaxies, the tightness of the infrared (IR)-radio continuum correlation is surprising. As the radio continuum emission at GHz frequencies is optically thin, this offers the opportunity to obtain unbiased star formation rates (SFRs) from radio-continuum flux-density measurements. The calorimeter theory can naturally explain the tightness of the far-infrared (FIR)-radio correlation but makes predictions that do not agree with observations. Noncalorimeter models often have to involve a conspiracy to maintain the tightness of the FIR-radio correlation. We extended a published analytical model of galactic disks 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 star-forming galaxies, 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 includes neither galactic winds nor CR electron secondaries, reproduces the observed radio continuum spectral energy distributions 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 2σ of the joint uncertainty of model and data for all datasets. The model agrees with the observed SFR-radio correlations within ∼4σ. Energy equipartition between the CR particles and the magnetic field only approximately holds in our models of main sequence star-forming galaxies. If a CR electron calorimeter is assumed, the slope of the IR-radio correlation flattens significantly. Inverse Compton 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 normal star-forming 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.