  We propose in this work a unified formulation of mixed and primal
discretization methods on polyhedral meshes hinging on globally coupled degrees
of freedom that are discontinuous polynomials on the mesh skeleton. To
emphasize this feature, these methods are referred to here as discontinuous
skeletal. As a starting point, we define two families of discretizations
corresponding, respectively, to mixed and primal formulations of discontinuous
skeletal methods. Each family is uniquely identified by prescribing three
polynomial degrees defining the degrees of freedom and a stabilization bilinear
form which has to satisfy two properties of simple verification: stability and
polynomial consistency. Several examples of methods available in the recent
literature are shown to belong to either one of those families. We then prove
new equivalence results that build a bridge between the two families of
methods. Precisely, we show that for any mixed method there exists a
corresponding equivalent primal method, and the converse is true provided that
the gradients are approximated in suitable spaces. A unified convergence
analysis is also carried out delivering optimal error estimates in both energy-
and $L^2$-norms.
