  We discuss a framework for understanding why spin glasses differ so
remarkably from homogeneous systems like ferromagnets, in the context of the
sharply divergent low temperature behavior of short- and infinite-range
versions of the same model. Our analysis is grounded in understanding the
distinction between two broad classes of thermodynamic variables -- those that
describe the global features of a macroscopic system, and those that describe,
or are sensitive to, its local features. In homogeneous systems both variables
generally behave similarly, but this is not at all so in spin glasses. In much
of the literature these two different classes of variables were commingled and
confused. By analyzing their quite different behaviors in finite- and
infinite-range spin glass models, we see the fundamental reason why the two
systems possess very different types of low-temperature phases. In so doing, we
also reconcile apparent discrepancies between the infinite-volume limit and the
behavior of large, finite volumes, and provide tools for understanding
inhomogeneous systems in a wide array of contexts. We further propose a set of
`global variables' that are definable and sensible for both short-range and
infinite-range spin glasses, and allow a meaningful basis for comparison of
their low-temperature properties.
