I discuss the conditions under which Higgs and confining regimes in gauge theory can be sharply distinguished. It is widely believed 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 both the confining and Higgs regimes, there is a novel order parameter which can detect certain Higgs-confinement phase transitions. This result is explained in the context of certain tractable gauge theories in three space-time
dimensions. Our observations significantly strengthen the case for the necessity of a phase transition between nuclear matter and quark matter in QCD, which we proposed in earlier work.