The polarizable density embedding model is combined with the multiconfigurational self-consistent field and MC-srDFT electronic structure methods to calculate solvatochromic shifts of the n-π∗ absorption of acrolein and the π-π∗ absorption of the para-nitrophenolate anion in aqueous solution. Differences between linear-response (LR) and state-specific (SS) solvent shifts are analyzed by assessing the contributions of different terms in the solvent potential. This comparison shows that the differences are not only due to the intrinsically different response of LR and SS excitation energies to the polarizability of the environment but also due to a different response to the static part of the environment potential. These observations show that even in nonpolarizable environments, LR and SS calculations based on SCF (orbital optimization) methods do not necessarily agree on the spectral shift. The difference can be as large as, or even dominate, the difference due to dynamical polarization.