I discuss the conditions under which Higgs and confining regimes in a gauge theory 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 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 spacetime dimensions. These observations significantly strengthen the case for the necessity of a phase transition between nuclear matter and quark matter in QCD.