Responding and reacting are often used as synonyms, interchangeable description of what one does after an event happens. The difference is easily explained when looking subjectively at a conversation.
One person speaks.
If the other person speaks immediately, as if automatic, or defensively, as if attacked, he or she is reacting. Reactions happen when you think you're in some sort of danger or need to defend something, often yourself.
You react when you let another's words get under your skin.
You react when you let another's opinions effect you.
Response happens when the other person listens for what is behind the words.
Listening for someone's beliefs, values, current struggles and opinions takes the words off of the listener. No matter what is said, a subjective reply (having no negative or positive energy to it) naturally occurs.
Responsiveness comes from moments of presence.
Reactions come from a person connecting past circumstance to the present or from a person worried and anxious for the future.
Being present allows us to rationally respond.
This is practiced easiest with those we don't know - the coffee shop clerk, the mailman, then with people we engage with - coworkers, clients, then with our friends and loved ones, and finally, with those we have animosity for.
Responsiveness not only diffuses arguments, it gives you room to forgive.