Outside vs Inside

I live in a hot climate so many times I have to suck it up and run on the treadmill.  It may be from oversleeping (which means it is too hot late in the morning to go outside) or childcare issues (my gym has a day care), there are occasions which call for a treadmill.  I use the treadmill exclusively for speed work and some people would consider that cheating.  The way I see it, I can go at any time of day and monitor my speed intervals and distance more accurately than outside.  While running on one the other day, I observed many other women around me at the gym doing the same, a thought occurred to me... What makes a runner?  Are you only considered a runner if you run outside?  If you sign up for races?  I see plenty of "runners" on the treadmills like myself and think if you run for fitness or just for the love of it, you are a runner.  I never considered myself a runner until I signed up for races though.  Once I started racing, especially distance races like the half and full marathons, I thought of myself as a genuine runner.    What do you think?