ABSTRACT: The relationship between classical variational SPN/GSPN formulations and asymptotic nonclassical SPN formulations is examined at the level of the governing reduced operators. In particular, the classical variational SPN operator is compared with the asymptotic SPN hierarchy obtained from the nonclassical spherical harmonics approximation (NSHA) applied to the nonclassical transport equation. It is shown that the SPN equations obtained from the classical variational formulation of Mishra et al. are recovered as the exponential free-path specialization of the NSHA-derived asymptotic operator hierarchy. In this limit, the moment-dependent nonclassical transport coefficients reduce to their classical forms and the NSHA-derived equations recover the classical SPN system exactly. When the free-path distribution departs from exponential form, the asymptotic NSHA formulation yields modified transport coefficients that cannot be recovered within the classical variational coefficient set. This operator-level comparison identifies the free-path moment conditions under which the classical variational formulation is recovered and clarifies how non-exponential free-path statistics modify the reduced SPN coefficient structure. Controlled numerical benchmarks compare classical and nonclassical SPN solutions for prescribed non-exponential free-path statistics. The calculations confirm coincidence in the exponential limit and demonstrate systematic coefficient-driven separation when the free-path moments depart from the classical exponential sequence. A deterministic GLBE reference-solution comparison is also included for the SP1 coefficient correction, illustrating the role of moment-informed coefficients in nonclassical reduced transport models. These results clarify the scope of the classical variational SPN formulation and provide a basis for selecting moment-informed SPN coefficients in deterministic transport calculations involving non-exponential free-path statistics.