  Diffeomorphism invariance is often considered to be a hallmark of the theory
of general relativity (GR). But closer analysis reveals that this cannot be
what makes GR distinctive. The concept of diffeomorphism invariance can be
defined in two ways: under the first definition (diff-invariance$_1$), both GR
and all other classical spacetime theories turn out to be diffeomorphism
invariant, while under the second (diff-invariance$_2$), neither do. Confusion
about the matter can be traced to two sources. First, GR is sometimes
erroneously thought to embody a "general principle of relativity," which
asserts the relativity of all states of motion, and from which it would follow
that GR must be diff-invariant$_2$. But GR embodies no such principle, and is
easily seen to violate diff-invariance$_2$. Second, GR is unique among
spacetime theories in requiring a general-covariant formulation, whereas other
classical spacetime theories are typically formulated with respect to a
preferred class of global coordinate systems in which their dynamical equations
simplify. This makes GR's diffeomorphism invariance (in the sense of
diff-invariance$_1$) manifest, while in other spacetime theories it lies latent
-- at least in their familiar formulations. I trace this difference back to the
fact that the spacetime structure is inhomogeneous within the models of GR, and
mutable across its models. I offer a formal criterion for when a spacetime
theory possesses immutable spacetime structure, and using this criterion I
prove that a theory possesses a preferred class of coordinate systems
applicable across its models if and only if it possesses immutable spacetime
structure.
