A woman's voice has a tighter quality. Vocal techniques are taught pretty much the same to prepubescent girls and boys, but they still sound different. The mechanics are the same, but it's a different quality of voice. Have you seen the musical Oliver!? The film version? Oliver's singing voice was done by a girl, and though she does a very good job of mimicking the boy soprano vocal quality, it's still not completely convincing if you're well-versed in this sort of thing. (I sang Where is Love at a concert when I was 7. It's not an easy song to sing...)
Once people hit puberty and their voices change, they have to re-learn how to use them. This goes for both men and women. Once again, the actual physical mechanics of how to find support and breath, and how to project your voice without amplification, in the case of classical singing, are more or less the same for both genders, they just sound different.