We derive covariant equations describing the tetraquark in terms of an admixture of two-body states D D (diquark-antidiquark), M M (meson-meson), and three-body-like states q q(T q q), qq(T q q), and q q(T qq ) where two of the quarks are spectators while the other two are interacting (their t matrices denoted correspondingly as T q q, T q q, and T qq ). This has been achieved by describing the qq q q system using the Faddeev-like four-body equations of Khvedelidze and Kvinikhidze [Theor. Math. Phys. 90, 62 (1992)] while retaining all two-body interactions (in contrast to previous works where terms involving isolated two-quark scattering were neglected). As such, our formulation, is able to unify seemingly unrelated models of the tetraquark, like, for example, the D D model of the Moscow group [Faustov et al., Universe 7, 94 (2021)] and the coupled channel D D − M M model of the Giessen group [Heupel et al., Phys. Lett. B718, 545 (2012)].