An operator is someone who operates (works, handles) a machine, switchboard, or any kind of apparatus: "a switchboard operator," "a telegraph operator," "a Linotype operator." As a noun, operative also means "a worker engaged, employed, or skilled in some particular task." What small distinction exists lies in the fact that operative is usually applied to someone engaged in a more skilled or subtle task than an operator: "He is an operative in the Treasury Department." "This spy spent years as an operative behind the Iron Curtain." As an adjective, operative means "effective," "workable": "Ordinances in this city are fully operative."
Dictionary of problem words and expressions. Harry Shaw. 1975.