Computer Science Degree vs Computer Engineer

You should be specific about the University that you are referring, as these terms may mean different things. But in general , they both really are the same terms.

Pursue a formal Computer Science program for a good foundation in Software Engineering. It teaches you the core of data structures, theoretical computer science, programming , Operating System etc.

Also a Computer Science course teaches the constructs of Electronics engineering including the basics of transistors , circuits and micro-controller programming. All of which are fundamental constructs for a career in hardware engineering.

Fundamental message is you will understand your own flair.

Computer engineering is more of a hybrid role that focuses on how computer science and electrical engineering come together. Computer engineering deals with hardware design. The engineer focuses on both the hardware and software aspects of technology. They study how the two interact together.