> About understanding how to control computers (which are fast electronic machines)

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

Computer Science is not about learning to make software, although it is usually a byproduct, as strong understanding of fundamental allows you to design software correctly from the first principle. Programming; however, is usually done through training at work.

Computer Science is about understanding what computation can and cannot achieve, and more importantly, how to achieve it (that is where it differs from Mathematics, where mathematicians are usually not interested in the how part). Under this definition, we can put typical college subjects into consideration:

* Data Structures and Algorithms: about studying how to manipulate data to solve a task efficiently.

* Complexity Theory: about formal classification of hardness of problems. What makes a computational problem "hard" or "easy"?

* Computer System: about how to construct a software system to achieve certain purposes. What are the constraints in a system (performance, security, privacy, correctness, fault tolerance, etc), and how to design a system to address such constraints? What tradeoffs to be made when you cannot meet all the desired requirements?

* Distributed System: how to design system with a few to massive number of computers that are connected in a network? How do you reason about fault tolerance, consistency, sharding, and so on?

* Operating System: about how to create abstraction to the hardware, that allows for other softwares to interact with it without having to explicitly deal with the hardware?

The list could go on, but I just give a couple of examples.

- Learning to make software in order to improves the lives of humans

This is not a discipline that I am aware of

- Learning to make software in order to make the lives of humans miserable

This is a discipline, but not quite Computer Science

- Learning to make software so that great engineers become average engineers, and incompetent engineers become managers

This is software engineering

There is also the part of CS that could be described as the science of computation.

The lines between academic fields are primarily administrative. Their main purpose is to facilitate undergraduate education. They are also fuzzy and vary between institutions. A person working in a CS department could find their home in the mathematics department at another university. Or physics. Or economics. Or biology. Or somewhere else. No matter what CS was at your university, it can be something very different at another.