Public Relations (P.R.) — "The profession or practice of creating and maintaining goodwill of an organization's various publics (customers, employees, investors, suppliers, etc.), usually through publicity and other nonpaid forms of communication. These efforts may also include support of arts, charitable causes, education, sporting events, and other civic engagements." (from businessdictionary.com)
P.R. can also be described as an organization's systematic plans and efforts to control and manage its image.
Publicity — "Type of promotion that relies on public relations effect of a news story carried usually free by mass media. The main objective of publicity is not sales promotion, but creation of an image through editorial or 'independent source' commentary. While the publicist can control the content of the story, he or she may not have any control over its placement or interpretation by the media." (from businessdictionary.com)