Using a sample of 215 supernovae (SNe), we analyse their positions relative to the spiral arms of their host galaxies, distinguishing grand-design (GD) spirals from non-GD (NGD) galaxies. We find that: (1) in GD galaxies, an offset exists between the positions of Ia and core-collapse (CC) SNe relative to the peaks of arms, while in NGD galaxies the positions show no such shifts; (2) in GD galaxies, the positions of CC SNe relative to the peaks of arms are correlated with the radial distance from the galaxy nucleus. Inside (outside) the corotation radius, CC SNe are found closer to the inner (outer) edge. No such correlation is observed for SNe in NGD galaxies nor for SNe Ia in either galaxy class; (3) in GD galaxies, SNe Ibc occur closer to the leading edges of the arms than do SNe II, while in NGD galaxies they are more concentrated towards the peaks of arms. In both samples of hosts, the distributions of SNe Ia relative to the arms have broader wings. These observations suggest that shocks in spiral arms of GD galaxies trigger star formation in the leading edges of arms affecting the distributions of CC SNe (known to have short-lived progenitors). The closer locations of SNe Ibc versus SNe II relative to the leading edges of the arms supports the belief that SNe Ibc have more massive progenitors. SNe Ia having less massive and older progenitors, have more time to drift away from the leading edge of the spiral arms.