To my way of thinking an athlete is determined by the approach they take to their sport. You don't have to be a winner of the genetic lottery and possess the innate physiology to be an elite athlete but you must be willing to do the work to make the most of the ability you do have. I guess you could say it's the difference between exercising and training. Set a realistic but challenging goal and shoot for it.
Personally I was an adult onset athlete. I played the usual sports as a kid but I wasn't particularly talented. I drifted away from sports and with them a healthy lifestyle. When I turned thirty I knew something had to change as I was sick and tired of being sick and tired. I quit smoking and drinking and started running. At first for fitness but when my GF at the time dragged me to a 5K I was hooked. Joined a running club and began to train for races. Not really gifted but I trained hard and was a solid upper middle of the pack runner at best. Won an occasional age group award. A big goal for me was to qualify for the Boston Marathon and it took me a few attempts to do it.
I took it a step further and got certified as a running coach and a personal trainer because I enjoy training and working with like minded folks. The athletes I admired and enjoyed working with the most were not the most talented but the most dedicated. My kind of people.
I got into riding seriously late in the game. I always rode but mostly it was when I was rehabbing from a running injury. That was until I had achillies surgery and fractured a hip. A hip replacement ended my running days. I had to do something so I brought a road bike and sort of applied the same structure to cycling as I did to running, ie intervals, tempo rides and a weekly long ride. I no longer compete but I still train just because I enjoy pushing myself and just riding around aimlessly bores me.
I've had a couple of other issues to deal with, cardiac ablation and shoulder surgery, but so far I'm still able to train hard enough to scratch my itch. I still enjoy getting into an impromptu throwdown with a couple of riding buds or a new friend on the road. I don't really know if I qualify as an athlete anymore but I'm just incredibly grateful to be able to swing a leg over the bike and get out there and work.