One way to think about the difference here is that proactive policing or proactive patrol is more of a crime prevention technique whereas reactive patrol or reactive policing is something that is done after a crime has already been committed.
Reactive patrol is more of a traditional style of policing. It consists of police waiting for a crime to be reported and then going to the scene to try to apprehend suspects. By contrast, proactive patrol attempts to prevent the crimes from happening in the first place. For example, a proactive patrol might be based on intelligence or statistical work that the police have done regarding when and where certain crimes are likely to take place. The police could then proactively patrol at the appropriate places and times to try to prevent crimes from happening.
There is a very fundamental distinction between proactive and reactive policing, with the former subject to controversy because of the nature of some police tactics that may be employed. Proactive policing simply refers to measures taken to deter crime or to eliminate or minimize the causes of crime. In that general sense, proactive policing is eminently worthwhile. For example, a regular police presence at a particular intersection deters traffic violations that would otherwise occur. Similarly, a regular police presence in certain neighborhoods minimizes the prospect of a crime occurring in those neighborhoods. Such proactive policing, then, is praiseworthy. The controversies arise when proactive policing extends to such measures as racial profiling, in which individuals are subjected to questioning or body- and car-searches solely on the basis of their ethnicity. Profiling is intended to prevent crimes by targeting individuals who "fit the profile" of those statistically more likely to commit a crime. Such tactics, however, often cross a boundary into unconstitutional procedures that may prevent a crime but that also victimize individuals who are not criminals but who merely meet the physical description of the category of individual statistically more likely to commit a crime. The Fourth Amendment of the U.S. Constitution protects Americans against "unreasonable searches and seizures," and proactive policing risks violating that fundamental tenet of civil liberties.
In contrast to proactive policing, reactive policing refers to the normal practice among law enforcement agencies of responding to crimes that are in motion or that have already occurred, such as reports of a burglary, rape or murder. Criminal investigations involve crimes that have already occurred, and forensic investigators exist to examine the physical evidence associated with the crime, such as hair fibers left by a rapist or murderer, fingerprints left by a careless burglar, and so on. In short, both proactive and reactive policing are integral to the mission of police departments, but the former can rest on more tenuous propositions if certain tactics intended to prevent crime cross the line into unconstitutionality.