It's not so much that it uses muscles differently. A treadmill creates the forward motion for you, so if you are 'running' with no incline, you're essentially just jumping up and down since you don't have to *push* yourself forward. In that respect running on a track is harder and as a result, burns more calories. HOWEVER, if you add a 1 or 2 percent incline to the treadmill, you can simulate the resistance of running on ground and a treadmill typically has a little more bounce which can be easier on the knees. This is how I train clients for marathons when they don't have 26 miles of road to run on.
So whichever you're most comfortable with. I prefer the treadmill/walkman because running in circles really does drag on after several laps. Parks are much more fun for outside running.