Ah, such a practical question. "Parkour." "Free-Running." Is there a difference? They certainly sound different, but does that actually mean anything?
As it turns out, the word, "Parkour," has French origins. The word began as, "Parcours," meaning route or course. This is an apt definition of what parkour has actually become. In general, parkour emphasizes the practical - how to navigate quickly and effectively through a (usually urban) environment riddled with obstacles and harsh terrain.
Free-running, on the other hand, is much more "showy." Whereas parkour, in theory, is simply about navigation from point A to point B, free-runners are flashy, and tend to showcase their skills and abilities in their movements. Think a lot of flips, tricks, and other jaw-dropping moves. Free-Running is about expression and theatrics through movement, according to Diffen.com.
There you have it. A basic analysis of the difference between parkour and free-running. Practicality versus art through movement.