  We consider relative Tor functors built from resolutions described by a
semidualizing module C over a commutative noetherian ring R. We show that the
bifunctors Tor^{F_CM}_i (-,-) and Tor^{P_CM}_i (-,-), defined using flat-like
and projective-like resolutions, are isomorphic. We show how the vanishing of
these functors characterizes the finiteness of the homological dimension
F_C-pd, and we use this to give a relation between the F_C-pd of a given module
and that of a pure submodule. On the other hand, we show that other relations
that one may expect to hold similarly, fail in general. In fact, such relations
force the semidualizing modules under consideration to be trivial.
