PR is the focused examination of your interactions and tactics and products and pricing that, when combined, determine what and how people talk about you. A publicity firm will tell you stories about how they got a client ink. A PR firm will talk about storytelling and being remarkable and spreading the word.
In my experience, few people have a publicity problem, but almost everyone has a PR problem.
MAC, Southwest, Walmart, Twitter, Google.
So, what's your story?