The ionization dynamics of the quantum systems with the Coulomb and short-range potentials in the presence of a strong radiation field is investigated. The features of the stabilization regime are discussed at various structures of the energy spectrum of the quantum system and the parameters of the radiation pulse. It is demonstrated that specific shapes of the atomic potential and the pulse parameters lead to either the interference stabilization or the Kramers-Henneberger stabilization. A relation between various stabilization effects and the conditions for them are analyzed.