Actually, Parkour and Free Running are two different "sports".
Technically, they are the same thing. The main and most important difference between the two is that Free Running has an emphasis on tricking and "show-off" while Parkour is all about getting from point A to point B in the shortest amount of time. I've been training Parkour quite a while ago, and dropped it since I was the only one training and because my environment is not that dense which prevents me from training correctly. Parkour in my personal opinion is a great sport because you train each and every part of your body.