Am I brown or white?

I haven't posted in a while but here is a good one to think about...

Everyone who knows me, knows that I have the cutest three year-old niece on the face of the Earth (not that I am biased or anything). I am so busy all the time that I don't get to spend as much time with her as I would like. When I do get to spend time with her, it is oh so precious to me.That being said, today I had the privilege of having her for a few quality hours.

DaNee' is mulatto; her mother is Caucasian and her father is African-American, so obviously her skin color is darker than mine. As we sat watching "Where The Wild Things Are", the following conversation took place between the two of us:

DaNee': Heather, I'm brown
Me: Yes you are
DaNee': Are you brown like me?
Me: No I am white
DaNee' (very confused): You're white?
Me: Yes
DaNee': But, your hair is brown
Me: Yes but my skin is white

She sat the rest of the day next to me, holding her arm next to mine comparing our skin color.

This intrigued me and left me wondering about the following questions: What goes on in the minds of little people? Did I confuse her? Was she talking about hair color or skin color?