  The property of color confinement ("C confinement"), meaning that all
asymptotic particle states are color neutral, holds not only in QCD, but also
in gauge-Higgs theories deep in the Higgs regime. In this talk we describe a
new and stronger confinement criterion, separation-of-charge confinement or
"S$_c$ confinement," which is an extension of the Wilson area-law criterion to
gauge + matter theories. We will show that there is a transition between S$_c$
and C confinement in the phase plane of gauge-Higgs theories, and we will also
explain what symmetry is actually broken in the Higgs phase of a gauge-Higgs
theory.
