is the prosecutor and the district attorney the same person

They could be the same person but not necessarily.  The district attorney is the elected offical in charge of prosecuting criminal offenses in the district.  A "prosecutor" is simply the general term used to describe a person who prosecutes criminal cases for the state, which could be either the DA or an assistant district attorney (ADA).  The DA's office often hires assistant district attorneys to handle big case loads since the DA cannot handle all of the cases alone.  DA's usually handle only high profile cases.  Thus, a prosecutor could be either the DA or one of his assistants who is prosecuting a given case.

I am a lawyer and practice in this area of the law.  The short answer is yes.  These are two different names for the person that has what is called prosecutorial discretion to determine what charges the state will and will not pursue.