Well, not really but in it's most simplistic form it isn't complicated. Just walking at a higher rate with a quicker pace and a bit harder breathing. There are so many things that complicate the run like VO2 Max, Interval Training, HRM Training, Diet, Supplements, the list goes on, that it is hard to get back to the root of what you are doing.
Keep it simple and realize what you are doing. Walking fast. Running. Lengthening your stride and increasing your turnover rate. Increasing your heart rate to maximize your fat burning potential while developing your oxygen intake efficiency and become a fitter, faster, runner. Oh wait... that was complicated. Just run.