It's a blurry line because I think that it depends a lot on talent. For example, I got started on running around the end of high school. I had been a competitive swimmer and done lots of other sports my whole life but didn't consider myself to be a runner. One day though, it struck me as a good idea to sign up for a local marathon, mostly for the challenge of finishing, not so much to compete. However, at the gun I found that I was running fairly effortlessly with the lead pack and went through 10k in 36 high and the half-way point in 1:19. Shortly thereafter, the leaders dropped me and my lack of fitness caught up to me as I eventually crawled across the line in 2:58. This was still good enough for top 10 at this event. I'm a competitive person and competed seriously in the race even though I hadn't trained seriously for it. Would that have made me more of a serious runner than the social runners who maybe train 50 miles per week but run the race easily with their jogging buddies?
This is perhaps an extreme example but what about high school athletes from low mileage programs who only run 25-30 miles per week but do loads of intervals. Surely they would count as serious runners more than somebody who does 40 miles a week all at very easy pace and runs races for social reasons and to do something for charity. I think that being a serious runner has more to do with your state of mind on race day than the amount of mileage you put in in your training.