Cytotoxic T cells recognize specfic antigens on the MHC sites to respond to an infection whereas NK cells are innate response and don't rely on antigen.
Their functionality is similar enough, but the major difference is that the T cells recognize antigens and NK cells do not. That is to say NK cells are the innate defense (first line) while cytotoxic T cells are cell-mediated and more specific.
Hope that helps