A quantum approach and classical molecular dynamics simulations (CMDS) are proposed for the modeling of rotational relaxation and of the nonadiabatic alignment of gaseous linear molecules by a nonresonant laser field under dissipative conditions. They are applied to pure CO(2) and compared by looking at state-to-state collisional rates and at the value of <cos(2)[θ(z)(t)]> induced by a 100 fs laser pulse linearly polarized along z[overhead arrow]. The main results are: (i) When properly requantized, the classical model leads to very satisfactory predictions of the permanent and transient alignments under non-dissipative conditions. (ii) The CMDS calculations of collisional-broadening coefficients and rotational state-to-state rates are in very good agreement with those of a quantum model based on the energy corrected sudden (ECS) approximation. (iii) Both approaches show a strong propensity of collisions, while they change the rotational energy (i.e., J), to conserve the angular momentum orientation (i.e., M/J). (iv) Under dissipative conditions, CMDS and quantum-ECS calculations lead to very consistent decays with time of the "permanent" and transient components of the laser-induced alignment. This result, expected from (i) and (ii), is obtained only if a properly J- and M-dependent ECS model is used. Indeed, rotational state-to-state rates and the decay of the "permanent" alignment demonstrate, for pure CO(2), the limits of a M-independent collisional model proposed previously. Furthermore, computations show that collisions induce a decay of the "permanent" alignment about twice slower than that of the transient revivals amplitudes, a direct consequence of (iii). (v) The analysis of the effects of reorienting and dephasing elastic collisions shows that the latter have a very small influence but that the former play a non-negligible role in the alignment dynamics. (vi) Rotation-translation collisionally induced transfers have also been studied, demonstrating that they only slightly change the alignment dissipation for the considered laser energy conditions.