It is one of the most challenging tasks at the Large Hadron Collider and at a future Linear Collider not only to observe physics beyond the Standard Model, but to clearly identify the underlying new physics model. In this paper we concentrate on the distinction between two different supersymmetric models, the MSSM and the NMSSM, as they can lead to similar low energy spectra. The NMSSM adds a singlet superfield to the MSSM particle spectrum and simplifies embedding a SM-like Higgs candidate with the measured mass of about 125.5 GeV. In parts of the parameter space the Higgs sector itself does not provide sufficient indications for the underlying model. We show that exploring the gaugino/higgsino sectors could provide a meaningful way to distinguish the two models. Assuming that only the lightest chargino and neutralino masses and polarized cross sections e(+)e(-) -> (chi) over bar (0)(i)(chi) over bar (0)(j), (chi) over bar (|)(i)(chi) over bar (-)(j) are accessible at the linear collider, we reconstruct the fundamental MSSM parameters M-1, M-2, mu, tan beta and study whether a unique model distinction is possible based on this restricted information. Depending on the singlino admixture in the lightest neutralino states, as well as their higgsino or gaugino nature, we define several classes of scenarios and study the prospects of experimental differentiation.