  In Bell scenario, any nonlocal correlation, shared between two spatially
separated parties, can be modeled deterministically either by allowing
communications between the two parties or by restricting their free will in
choosing the measurement settings. Recently, Bell scenario has been generalized
into `semi-quantum' scenario where external quantum inputs are provided to the
parties. We show that in `semi-quantum' scenario, entangled states produce
correlations whose deterministic explanation is possible only if measurement
independence is reduced. Thus in simulating quantum correlation `semi-quantum'
scenario reveals a qualitative distinction between signaling and measurement
dependence which is absent in Bell scenario. We further show that such
distinction is not observed in `steering game' scenario, a special case of
`semi-quantum' scenario.
