You need to be careful here. At least in the US, the most common meaning of “I’m not that kind of girl” is “I’m not the kind of girl who will have pre-marital sex.” This use of “I’m not that kind of girl” may be a bit old-fashioned and is a bit of a cliche, but it is immediately what I think of when I read that phrase.

I don't think so. In the first case is can be understood you are talking about the kind of girl, but it can also mean other things, like for example you find a girl you think you know from school years ago, and then ask her if she remembers you and she says "I'm not the girl that you think I am" to put an example. Another choice for the second sentence would be "I'm not the type of girl you think I am"