The term plaintiff is from civil
law. The kind of case you are talking about is criminal
law. The entity going against the defendant is the state, as represented by the District Attorney (or, most of the time an Assistant District Attorney).
Rights differ. Defendants are protected more rigorously in criminal cases because people's freedom and sometimes their lives, are at stake, whereas in civil cases it's almost always money and property that are at stake (there are lots of exceptions but the gist of it is that the penalties in criminal cases are inevitably a lot higher).