Computer Scienceis the study of computation. It informs how we create software (ideally). Topics might be: Complexity, algorithms, models of computation, automata,  It is arguably a branch of discrete mathematics, and builds upon set theory, logic, etc.

Computer Engineeringis studying how computing machines are built. It informs how we build hardware. Topics might be: Hardware architectures, gates, instruction set design, digital communications  It overlaps digital electronics and physics.