In this study, the causes of biaxial and hydrostatic stress components in epitaxially grown thin GaN films on sapphire are analyzed. It is observed that growth by Molecular Beam Epitaxy (MBE) and by Metal Organic Chemical Vapor Deposition (MOCVD) are governed by very similar physical principles. Differences in the absolute stress values are mainly due to the difference in growth temperature. It is argued that in the case of MOCVD growth the onset of plasticity for higher growth temperatures is responsible for a larger stress relaxation in the buffer layer. It is further found that either process can result in highly off-stoichiometric GaN layers, as manifested by the large variations in the a and c lattice parameters caused by intrinsic point defects.