Although some people still argue about what is what, and some people think that the name is not important, I thought you might like the defnition, as described by 3run:
"Free-running: the art of expression through motion. Free-running takes the basic skill sets of each of the other three disciplines [parkour, tricking, street-stunts], and combines them into a single activity. "Free-runners" often take part in parkour-like runs, but are freed from the efficiency restriction, and so include spins, flips, and direction reverses to increase the overall aesthetic appeal of the run. They also utilize single obstacles after the manner of stuntmen, and sometimes perform tricking combos off of those obstacles. There are no rules at all in free-running; the goal is to achieve a sense of personal freedom and satisfaction with your technique. However, a typical free-runner will be proficient at a wide range of vaults, able to take medium to large-sized drops with a roll, and good at several different kinds of flips, especially the front flip and the basic wallflip. A free-running video usually follows one or more free-runners in fairly constant motion throughout an environment, with occasional pauses for techniques like handstands, flag holds, and flips from stationary positions on obstacles. Free-running videos will include absolutely any kind of location, from safe environments like a gym or a pool or a sandpit to urban environments like an escalator or a rooftop to natural environments like a forest or a cliff.
