  We discuss the conditions under which Higgs and confining regimes in gauge
theories with fundamental representation matter fields can be sharply
distinguished. It is widely believed that these regimes are smoothly connected
unless they are distinguished by the realization of global symmetries. However,
we show that when a $U(1)$ global symmetry is spontaneously broken in
\emph{both} the confining and Higgs regimes, the two phases can be separated by
a phase boundary. The phase transition between the two regimes may be detected
by a novel topological vortex order parameter. We first illustrate these ideas
by explicit calculations in gauge theories in three spacetime dimensions. Then
we show how our analysis generalizes to four dimensions, where it implies that
nuclear matter and quark matter are sharply distinct phases of QCD with an
approximate $SU(3)$ flavor symmetry.
