Computer Science is the general term that includes all the other computer related majors within it.
If you mean what is the difference between the orientation and focus of computer science that is taught in science vs. engineering colleges (in some countries around the world), then I would say that the computer scientists are closer to software, mathematics, and theory whereas computer engineering is closer to hardware and physical systems development with hands on skills.
But in today's world, the difference is really subtle and both computer scientists and engineers are working together in teams to complete each other.