What is the context? I think that if a policeman is on beat, it means he's on duty. On the other hand, the "beat" means the "rythm". Reporters can also work "on a beat".
I think a policeman can be on duty without being "on a beat" - "on a beat' means that he is following a specific route that he is asigned to. (So, he could say "I'm not on a beat - I'm working in the station this week.")