We argue that there is an essential and gauge invariant distinction between the Higgs and confinement phases of a gauge Higgs theory, in terms of both symmetry and type of confinement, when the scalar field is in the fundamental representation of the gauge group. The Higgs phase is the spin glass phase of a gauge Higgs theory, in which custodial symmetry and a global center subgroup of the gauge symmetry are spontaneously broken. Although the asymptotic spectrum consists of color singlets in both the confinement and Higgs phases, the confinement phase satisfies a generalization of the Wilson area law criterion which we call "separation of charge" confinement, while the Higgs (spin glass) phase does not.