We employ mean-field lattice density functional theory to investigate the phase behavior of a binary (A-B) mixture confined to nanoscopic slit pores with chemically homogeneous walls. We consider only nearest-neighbor interactions in symmetric mixtures, where epsilon(AA)=epsilon(BB) not equal epsilon(AB) and epsilon is a measure of attraction between molecules of like (subscripts AA and BB) and unlike species (subscript AB), respectively. In addition, molecules are exposed to short-range attraction by the substrates separated by z lattice planes where epsilon(W) is the relevant coupling parameter. Moreover, the chemical potentials of both components are the same, that is, mu(A)=mu(B)=mu. In thermodynamic equilibrium (for fixed temperature T and chemical potential mu) the grand-potential density omega[rho,m] (rho identical with [rho(1),...,rho(z)], m identical with [m(1),...,m(z)]) assumes a global minimum which we find by minimizing omega numerically with respect to the order parameters rho(l) identical with rho(A)(l)+rho(B)(l) (total local density) and m(l) identical with (rho(A)(l)-rho(B)(l))/rho(l) (local "miscibility") at lattice plane l parallel to the pore walls. By varying epsilon(AB) three generic types of bulk phase diagrams are observed. On account of confinement (i.e., by varying epsilon(W) as well as z) one may switch between these different types of phase diagrams. This may have profound practical repercussions for experimental nanophase separation since depending on pore width and chemical nature of its walls a bulk gas mixture may undergo capillary condensation and form either a stable mixed or demixed liquid phase.