In the present work, we have performed systematic studies of nuclear reactions of various light and medium mass nuclei (He, Li, Be, B, C, Ca, Ni, Zr and Sn isotopes) on $^{12}$C and proton targets mainly at high energies using Glauber model and a comparison of the results with available experimental data is made. The microscopic nuclear densities needed for these calculations have been obtained using relativistic Hartree–Bogoliubov formalism. In addition, other ground-state bulk properties are also calculated and compared with the available experimental data. It has been observed that the results obtained using the relativistic framework with the density-dependent meson exchange (DD-ME2) parameter set are in better agreement with the experimental data than with the density dependent point coupling (DD-PC1) results. Also, we have seen that the total reaction cross-section increases with the increase of the projectile mass. The differential elastic scattering cross-section results obtained with both parameter sets are almost identical at low scattering angles and compare well with the experimental data. However, at higher scattering angles, they show significant differences from the experimental data.