There are two main differences that we can identify that make private security forces different from official police.
The first difference has to do with the scope of their objectives. The police, of course, are charged with preserving the peace for the entire society. They are trying to ensure that all people in a given community will be safe from criminal activity. By contrast, private security forces are generally concerned with a much more limited group of people (or property). They do things like guarding specific buildings or gated communities. They are not very much concerned with the welfare of the overall society.
The second difference has to do with what they are trying to accomplish for their “clientele.” While this statement is not 100% valid, we can say that police are more concerned with investigating crimes and arresting criminals. By contrast, private security forces are only interested in preventing crime. Private security forces conduct intensive patrols of specific areas as a way of preventing crime from happening in the first place. Police cannot typically provide that kind of prevention and have to concentrate, instead, on responding to and investigating crimes that have already happened.