When does one become a runner?

I have been in a transition phase with my workouts as of late. The shift has moved me away from the intense gym sessions filled with machines and free weights toward a more natural yoga and running centered routine. This morning I woke up after a very restful Saturday ready to conquer an outside run. It has been rainy and gloomy in D.C. this weekend, but I had already decided on a run, and I am not one to back down. So off I went, intending to conquer the same trail I have been running for the past two weeks. Except today, I want to push harder, run farther, and feel more accomplished. Everything started out fine, but by the 4th song I started having pain in my left shin. I slowed to a walk and tried to mentally overcome the pain to keep going. But it just wasn't happening. I turned around about a quarter of a mile from last weeks stopping point. Frustrated, I pushed myself to get back in a respectable time by doing run walk splits. I used the 90 second run/30 second walk variation and was feeling alright by the time I got back to my area of town. I decided to keep going and jogged around some beautiful embassies for a little while. I was gone for just over an hour, and I assume I did around 3.5 to 4 miles. Not bad, but not what I was expecting either. I came home and did yoga for runners via yogadownload.com to try and work out some of the tightness in my shins.I also ate this upon returning, which is a combination of leftovers from the weekend.
My run today has me thinking a lot about what it means to be an athlete, or more specifically a runner. I don't subscribe to the idea that you have to enter races, or even train for specific events to justify calling yourself an athlete. I believe it is a personal thing. I find motivation when I hear someone call me "athletic" or ask where/how/when I run. It really has nothing to do with owning the right clothes and gear. It has to do with making the choice to move instead of sit, to eat whole foods instead of processed junk, and listening to your body instead of pushing beyond a certain limit. Yes, sometimes (most of the time) that means dessert with lunch on a Sunday. I coin the above "Ice Cream in a Jar" as opposed to the usual "Oats in a Jar."
In all, this post is a tangent, but I have been considering signing up for a 1/2 marathon in October, so running has been on my mind a lot lately.
I would love to know what anyone out there reading defines as "athletic," or what it means to you to be a runner.
~Jenn