Science as in Computer Science:
Primary focus is on software programming, but also delves all the way down to machine code, so basically early computer hardware so that there is an understanding from the ground up (Operating system development is usually part of the curriculum). Very heavy on math and the science of computation, in other words, the techniques behind WHY computers work and how to solve problems without writing any code (ie, can you build a computer or program to solve a problem in a useful time period? No point in building a system if it will take 40 years to arrive at an answer that is only useful next week)
Engineering as in Computer Engineering:
Usually overlaps heavily with the above, but focuses on designing the actual hardware systems in the end. So will have additional training in electrical engineering concepts, but focusing on digital and not analog circuit design, typically. I know some schools have the first two years of any engineering degree take basic engineering principles (Math, Physics, Material Science, etc)
Information Systems
Can be heavily focused on database programming, but also dealing with information exchange between different systems. So effectively combining the efforts of the above two disciplines into a more application focused discipline. Honestly there are so many paths in here that fall under the name it will likely differ greatly between educational institutions and regions.
What it really comes down to is foundational knowledge. An IS, CS, or CE degree will get you in the door somewhere, but it is up to you to tailor your own interests and education to suite what you want to do. You might wind up in a standard IT role, management, etc. The key is the education and credentials to get started. I personally know a MS Chemistry graduate, a BS Electrical Engineering graduate, an AS in Etymology (insects) (former Aerospace Engineering) (started out working IT in a pest control company), Real estate agent (still not sure how that one happened), all in IT positions at a fortune 500.
As a prime example I like to use my brother. He was always interested in electronics, so he pursued a degree in EE, but went down the path of biomedical electrical engineering, thinking there would be a future in the electromedical industry (and there certainly is) However, while learning motion control techniques caught his attention and he ended up learning a lot about designing electronics for things in motion. Ended up working at flight simulator company. So didn't even stick down the path he chose, and the same can easily happen to you, you might find something you really like while studying information systems, or simply take what you learned and apply it to something completely different like some of my former colleagues.
Of note I am career IT. Wanted to do desktop repair like so many others here, not a whole lot of a market since computers have more or less become disposable to the general public. But I ended up doing software asset management at a big company. So basically I learned 90% of my skills on the job and my background in electronics and computers lets me think very logically about problem solving (which is way more than half of IT jobs)