Chloride is the name for the Cl- ion. Since most things are soluble in water, almost any chloride (for example, table salt, NaCl) will contribute Cl- to the solution. AFAIK elemental chlorine is not actually used as a disinfectant; water treatment plants probably use hydrochloric acid (HCl) which in water tends to dissociate into H+ and Cl-.
And yes, campden will strip out chlorine and chloramines. It will actually increase chloride (and sulfate) concentration.