You're awesome is what your are!
As to whether you're a runner... Do you feel like a runner? I ran all last year, ran barefoot, ran a 5k with the family, but I wouldn't call myself a runner. It's not part of my psyche. My husband runs 4 or so miles on his work days; he is pondering now at what point he would consider himself a runner. He has all seasons of running clothes, though.
He votes for running clothes (and is now expounding on how much he loves the running shorts I had to talk him into buying). I do too! Call it gear to further your performance. (now he's questioning your sanity, what with the hills in Maine... He hates running in Rumford & Byron when we're up ;) )