An ex-con is a person who has completed a term in a prison and is now free. A prisoner is someone under detention, it could be by soldiers or police. An inmate is a person held inside an institution of some type. You could be an inmate of a prison or a mental institutions. Some writers might use the term inmate to infer that some workplaces are like institutions. as "When he was at work, he felt at home with the other inmates'