  We compare and contrast various relative cohomology theories that arise from
resolutions involving semidualizing modules. We prove a general balance result
for relative cohomology over a Cohen-Macaulay ring with a dualizing module, and
we demonstrate the failure of the naive version of balance one might expect for
these functors. We prove that the natural comparison morphisms between relative
cohomology modules are isomorphisms in several cases, and we provide a
Yoneda-type description of the first relative Ext functor. Finally, we show by
example that each distinct relative cohomology construction does in fact result
in a different functor.
