Although both computer engineering and computer science focus mainly on computers, the major differentiating factor is that both courses focus mainly on different aspects of computers. Computer Engineering simply refers to a branch of engineering that focuses mainly on the practical aspect of computers, i.e., the design and application of computers.
Computer Science, on the other hand, refers to the study of computers and their languages, mathematical structures that relate to computers. Computer science focuses mainly on how different software in a computer is designed and how they perform their specific tasks. Computer science, as a course, is deeply rooted in different mathematics operations.
Computer science is a program mostly studied in the College of Arts and Sciences, while computer engineering is a department on its own in the college of engineering. Most computer hardware is built by computer engineers and not by computer scientists. In the same vein, most computer software is built by computer scientists and not by computer engineers.