I will 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, I will show that when a U(1) global
symmetry is spontaneously broken in 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. I'll illustrate these ideas by
explicit calculations in gauge theories in three spacetime dimensions,
and then explain the generalization to four dimensions. One important
implication of our results is that nuclear matter and quark matter are
sharply distinct phases of QCD with an approximate SU(3) flavor
symmetry.