  The effective field theory of massive gravity had long been formulated in a
generally covariant way arXiv:hep-th/0210184. Using this formalism, it has been
found recently that there exists a class of massive nonlinear theories that are
free of the Boulware-Deser ghosts, at least in the decoupling limit
arXiv:1007.0443. In this work we study other recently proposed models that go
under the name of "gravitational Higgs theories" arXiv:1002.3877,
arXiv:1008.5132. We show that these models, although seemingly different from
the effective field theories of massive gravity, are in fact equivalent to
them. Furthermore, based on the results obtained in the effective field theory
approach, we conclude that the gravitational Higgs theories need the same
adjustment of the Lagrangian to avoid the ghosts. We also show the equivalence
between the noncovariant mode decomposition used in the Higgs theories, and the
covariant St\"uckelbergization adopted in the effective field theories, thus,
proving that the presence or absence of the ghost is independent of the
parametrization used in either theory.
