Generally, Universities design their degree plan based on industry requirements and it is always changing. However in present days if you decided to take Computer Science the path you will be taking focuses more on programming languages, protocols, problem solving using algorithms, and lots of theories on all of those above stuffs. You will not worry about about how the Processors are designed and built, how RAMs are built, how screens produce their colors, none of those although they are a monumental task themselves. In fact you have a simple code say in C language: “printf(“Hello World!”)” and this code will be translated into assembly language and then to machine language all by the CPU with the help of RAM as a memory to remember the code and directs the screen to print the pattern and then the screen turns on the required pixels on your screen to respective colors. There is a lot of thing happening on one simple code both in hardware and software level. To make it happen you will need a lot of knowledge and manpower and so all types of people with all types of knowledge are required for companies. And there are places where both of those layers tries to overlap at least in the context of human understanding. For example when designing assembly languages, compilers, device drivers and kernels one need to have some or detail knowledge of the hardware that being worked on.
To wrap it up, Computer Scientists utilize the raw power of computers (silicon made logic chips) without their deeper understanding to solve problems in human lives like commerce, medicine, entertainment and so on with the help of programming language and algorithms.
And Computer Engineers are those who make it all possible by designing and innovating to make better and powerful CPU’s and system for task automation including other peripherals and required components in simple terms hardware.
Not just computer scientist and engineers but without the contribution of Physicists and Mathematicians the present day Computers would be impossible to achieve