- Computer Science is 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 Engineering is 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.
So you see the word “computer” in “Computer science” is something of a misnomer. Perhaps “Computing science” might be more accurate.