Computer Systems Engineering
> About inventing programming, from the ground up. (A weird sub-discipline of mathematics and category theory)
Computer Science
> Learning to make software in order to improves the lives of humans
Software Engineering
Otherwise, where do operating systems fall? Are they systems engineering? They don't seem to be entirely about the hardware to me, and they were a core part of my CS program. What about SeL4 - which is a formally verified operating system project?
How about programming languages like C or Rust? Is that computer science, or systems engineering? How about Excel - the world's most popular programming language - that happens to be functional? Are financial planners doing computer science when they program a spreadsheet?
The lines are blurry everywhere. My CS program offered 3 different degrees, like you said - Computer engineering, Computer Science and Software Engineering. The only difference was the CS degree had a lot of electives, and the other two filled those electives in with (different) required subjects.
Maybe CS is just "lets play with some cool things on computers!". And there's a big playpen of things to explore. Thats more or less how it feels to me.