With respect to 'Art of motion' being a nickname for Parkour, I don't think that idea is supported by any sources, reliable or otherwise. BlackDragon posted a list of links on my talk page:  
 *https://www.facebook.com/pages/Art-Of-Motion-ParkourFreerunning-class/154047511368505 
 *http://www.redbull.com/cs/Satellite/en_INT/Art-of-Motion/001242981743204 
 *http://adventure.howstuffworks.com/outdoor-activities/urban-sports/parkour.htm 
 *http://www.prnewswire.com/news-releases/red-bull-art-of-motion-brings-parkour-stateside-101882433.html 
 *http://www.youtube.com/watch?v=nerrZgFvo40 
 *http://www.youtube.com/watch?v=by7uU_yUvxA 
 *http://www.youtube.com/watch?v=AZAeuchfRP0 
 *http://www.youtube.com/watch?v=m0PNn4rc_II 
 *http://www.redbull.com/cs/Satellite/en_INT/Event/Red-Bull-Art-of-Motion-Santorini-021243224470771 
 ...none of which show 'Art of motion' being used as a nickname for Parkour. Seven of the sources show 'Art of motion' being used as the name of a Red Bull event, one is a facebook page for someone running, and I quote, "Art of motion class (Similar to Parkour/Freerunning)", the 'howstuffworks.com' article doesn't even mention the phrase 'art of motion', instead saying "Parkour is an international discipline, sport and hobby that is best described as the art of forward motion in spite of obstacles, or to put it simply: the art of movement." All of them that actually mention the phrase 'art of motion' say that it is something different. I therefore see no evidence to support 'art of motion' being a nickname for Parkour.