I believe, though I don't speak chinese, that Bai Hao refers to the varietal, while the tea class has to do with when it's harvested and how it's processed.
Those teas are both really strong examples of the respective classes, but are otherwise totally different.
The white: http://www.teaspring.com/Bai-Hao-Yin-Zhen.asp The oolong: http://www.teaspring.com/Bai-Hao-Oolong.asp
I believe, though I don't speak chinese, that Bai Hao refers to the varietal, while the tea class has to do with when it's harvested and how it's processed.
Those teas are both really strong examples of the respective classes, but are otherwise totally different.