  We explore the relationship between Kochen-Specker quantum contextuality and
Bell-nonclassicality for ensembles of two-qubit pure states. We present a
comparative analysis showing that the violation of a noncontextuality
inequality on a given quantum state reverberates on the Bell-nonclassicality of
the considered state. In particular, we use suitable inequalities that are
experimentally testable to detect quantum contextuality and nonlocality for
systems in a Hilbert space of dimension $d=4$. While contextuality can be
assessed on different degrees of freedom of the same particle, the violation of
local realism requires parties spatially separated.
