The relation between the resolved star formation rate (SFR) per unit area and the nonthermal radio continuum emission is studied in 21 Virgo cluster galaxies and the two nearby spiral galaxies, NGC 6946 and M 51. For the interpretation and understanding of our results, we used a 3D model where star formation, 2D cosmic-ray (CR) propagation, and the physics of synchrotron emission are included. Based on the linear correlation between the SFR per unit area and the synchrotron emission and its scatter, radio-bright and radio-dim regions can be robustly defined for our sample of spiral galaxies. We identified CR diffusion or streaming as the physical causes of radio-bright regions of unperturbed symmetric spiral galaxies as NGC 6946. The enhanced magnetic field in the region of interstellar medium (ISM) compression via ram pressure is responsible for the southwestern radio-bright region in NGC 4501. We identified the probable causes of radio-bright regions in several galaxies as CR transport, via either gravitational tides (M 51) or galactic winds (NGC 4532) or ram pressure stripping (NGC 4330 and NGC 4522). Three galaxies are overall radio dim: NGC 4298, NGC 4535, and NGC 4567. Based on our model of synchrotron-emitting disks, we suggest that the overall radio-dim galaxies have a significantly lower magnetic field than expected by equipartition between the magnetic and turbulent energy densities. We suggest that this is linked to the difference between the timescales of the variation in the SFR and the small-scale dynamo. In NGC 4535, shear motions increase the total magnetic field strength via the induction equation, which leads to enhanced synchrotron emission with respect to the SFR in an otherwise radio-dim galactic disk. Radio-bright regions frequently coincide with asymmetric ridges of polarized radio continuum emission, and we found a clear albeit moderate correlation between the polarized radio continuum emission and the radio/SFR ratio. When compression or shear motions of the ISM are present in the galactic disk, the radio-bright regions are linked to the commonly observed asymmetric ridges of polarized radio continuum emission and represent a useful tool for the interaction diagnostics. The magnetic field is enhanced (as observed in NGC 4535 and NGC 4501) and ordered by these ISM compression and shear motions. Whereas the enhancement of the magnetic field is rather modest and does not significantly influence the radio-SFR correlation, the main effect of ISM compression and shear motions is the ordering of the magnetic field, which significantly affects the CR transport. Cosmic-ray energy losses and transport also affect the spectral index, which we measured between 4.85 and 1.4 GHz. The influence of CR losses and transport on the spectral index distribution with respect to the synchrotron/SFR ratio is discussed with the help of model calculations. Based on our results, we propose a scenario for the interplay between star formation, CR electrons, and magnetic fields in spiral galaxies.