You might equate "score" with "reputation", but that's not what the system does. Reputation is just reputation, whether you want to call it "points" or "mojo" or "large arbitrary numbers". This is not unlike how one might refer to the conclusion of a question (in getting a good answer) as "closing" the question, whereas the system uses "closing" to refer to something different. Yes, it might be confusing if you interpret it that way, but at the end of the day "closed" still means a question that no longer accepts questions, and the same goes for the meaning of "score" being defined as something that isn't reputation.
Score is used to refer to the number of the upvotes on a post minus the downvotes. Referring to the displayed number as "upvotes minus downvotes" is pretty bothersome after a while, and we use that value in a lot of calculations: lots of badge requirements, post visibility on the front page, bounty auto-award, deletion prevention, and much more. So a term is very useful to have, and "score" representing the effective value is a fairly appropriate term.