When did I stop being a girl?

Yesterday at the gym someone said something funny. It wasn't funny "ha-ha" it was more of a "it gave me a funny feeling" sort of funny. I wanted to use the ab machine thingy when another guy stepped up to it. We did the required dance of "Oh shucks, I needed that. It's ok, I'll wait" "Oh, you sure? You can go ahead" "Oh no no no, it's quite alright, you go ahead." Anyway, I let the guy go ahead of me.
When he was done he wiped it down while I waited. I made a comment about it and he said something like "Well I usually don't unless someone is following me right away. Especially since you're a woman I needed to look good." On the one hand his honesty made me laugh, on the other I laughed to myself and thought "Ha, he called me a woman."
It's weird. Even though I'm 20 years old, live on my own, work and pay my own bills it still feels funny to think of myself as a woman and not a girl. When I think of a woman I think of a grown up. As independent as I may be it's still funny to think of myself as an adult. The guy must have been in his late 20s so it's easy to see why he'd think of myself as a woman and not a girl. I mean, it's not like he's an old man compared to me. It's still strange to hear someone referring to me like that, though.
Not to get all Britney Spears on the subject (after all, who didn't hate that song?) but if I don't think of myself as a woman and I'm definitely not a girl anymore then what the hell am I?
Earlier this week another guy at the gym made another comment to that effect. Something about me looking like a "real woman" (Boy, that was awkward when I told him I have a boyfriend). It was supposed to be some sort of pick me up after another chick who looked like she was 16 but was almost 30 said I looked like I could be her age. I said I didn't take it as a compliment to be told I look older than I really am and the guy said it's better to look like a real woman than a child. Meh... I think it has something to go with my refusal (i.e. fear) to grow up. I've never been in a rush to grow up so maybe that's why it's not easy for me to identify myself with the word "woman." It's not a gender thing. In that respect (gender) I am a WOMAN. But in the girl/woman definition based on age and maturity well, I'm still quite a child. Weird...