When you respond, you are no longer being controlled by the event; you are taking measures to control it. Reacting without thinking creates yelling matches. Responding creates useful dialogue. I have learned the hard way that you can't stop your emotions and to try to do so would be counterproductive. The trick is to control what you do with them. It is a lesson that ought to be stressed early in everyone's career.
Understanding the Difference
A good analogy revolves around fear and danger. In a dangerous situation, fear inevitably pops up and creates a powerful emotional response that if left unchecked can cause you to run, freeze, or shutdown altogether. If allowed to fester, fear becomes your reaction to the danger, which leaves you wide open to its full effects; the exact opposite of what you want to happen. You need to focus on formulating a response that gives you a way to deal with the danger.
Our thoughts are what drive us. How we look at something helps define our actions. If you allow poking the bear to control you, then all your conflicts become a nail, and all your solutions become a hammer. That is not law enforcement but a battle of testosterone levels.
A simplified example of responding vs. reacting would be what might happen during a traffic stop. We have all been there where the person being stopped goes on a tirade about why you stopped him. Inevitably, his conversation always goes south and includes something about doughnuts, what part of the male anatomy you are, how he pays taxes and therefore your salary, and that he knows your CEO personally.