Nuclear Science is the study of nuclear processes. Right now the key areas are nuclear fusion and gamma ray spectroscopy. Nuclear Engineering is the application of science to design and operate power plants and certain kinds of imagers, primarily.
A Nuclear Scientist typically has a Ph.D. in Physics. A Nuclear Engineer typically has an M.S. or Ph.D. in Nuclear Engineering. The funding in the United States has been declining for Nuclear Science for a long time so it is a challenge to find work. I have no idea about the prospects for Nuclear Engineering. Maybe someone here knows more.