Strictly speaking, I would agree with the definitions provided by yuyan不通. Thin is used to describe 2D objects or a profile; skinny is used to describe 3D objects or forms. BUT, I think this misses the context of the question. In the vernacular, thin and skinny are both commonly used to describe a person's body. I think this is the context of Yi-Ying's question.
In this case, I would argue that the terms 'thin' and 'skinny', to describe someone's body shape, are very nearly the same. 'Thin' to me has a slightly more positive connotation; 'Skinny' is used to describe younger people (children) or if used to describe adults, has implies a slightly more negative meaning. Perhaps the most positive way to describe a person's body is the term 'slender'.