Yes, the medium hair gene and the longhair gene is the same.So, is she carrying the long hair gene?
Why some cats get longhair but some mediumhair? As I understand it, there also other genes playing.
"Helpgenes" if you so want.
If you plan to breed on her, I wouldnt advise it. She is nice, but the world is full of nice moggies whom desperately need a home...