We propose a unified asymptotic approach in order to derive the Oberbeck-Boussinesq approximation from the compressible Navier-Stokes equations coupled to a heat equation with an eventual source term. We point out, in the configuration of a horizontal infinite layer, the conditions for the density changes to be small, first for an ideal gas and then for a fluid with a divariant state law. We identify two small parameters. The original equations are then non-dimensionalized with different characteristic pressures and different linearized state laws for ideal gases and for a general fluid. We can either let the two small parameters go to zero and formally derive the asymptotic system of equations whereas in the gaseous case, we can directly use the Low Mach Number asymptotics. The coherence between the two approaches is provided and the link with the entropy production is established. It is emphasized that, in some situations, the work of the static pressure forces has to be retained in the final set of equation with both strategies since it involves the ratio of the two small parameters. It is related to the static pressure stratification of the fluid and can not be eliminated directly even if it is usually neglected in the Oberbeck-Boussinesq approximation. This original result proves the necessity to start from a divariant state law instead of the usual assumption that the density only depends on the temperature. Finally we prove, using a linear stability analysis and numerical simulations that this term has a stabilizing effect on the Rayleigh-Bénard problem and can even suppress the onset of natural convection for some values of the parameters.