Dear Monica,
About your question... I would guess they are the same thing. I know Wudan and Wudang are the same. Wu Tang might be different.

The problem is of course that we Americans tend to bastardize any language. For example, "Kung Fu" is actually from the Chinese "gongfu," which can literally be translated to "the study of work." Of course it implies much more than that and can have several meanings... Because it is difficult to perceive another languages' subtle pronunciation, we make the consonants harder, thus g becomes k and d becomes t (common changes). (By the way I am a language teacher - Spanish - which is partially why I know these things)
I am sorry I cannot give you a 100% sure answer, but hopefully I have "enlightened" you a little.

have a nice day!