We study the relation between two order parameters for deconfinement, normally employed in the literature: the continuum threshold s0, in the context of QCD Sum Rules, and the trace of the Polyakov loop ϕ in the framework of a nonlocal SU(2) chiral quark model. We establish a bridge between both order parameters at finite temperature T and baryonic chemical potential μ. In our analysis, we also include the the chiral quark condensate, the order parameter for the chiral symmetry restoration. We found that s0 and ϕ provide us with the same information for the deconfinement transition, both for the zero and finite chemical potential cases. At zero density, the critical temperatures for both quantities coincide exactly. This part of the analysis has been reinforced by the discussion of the corresponding susceptibilities and the static quark entropy behavior. At finite μ both order parameters provide evidence for the appearance of a quarkyonic phase.