Correct; furthermore, in a lot of major languages, Korean included, "Yes" means you agree with the question-statement. In English, this causes ambiguity, which then requires a supplementary clause to define the "yes" further, which is why most speakers use "no" in a negative question. Compare: "You don't want coffee?" English - "Yes (???)" / "No (I don't)" / "No, I do" Korean - "네 [Yes] I don't want coffee"
Slavic languages do this too, to the best of my knowledge. Some Germanic languages as well.
The difference between 네 and 예, is the polite. the word 네 is informal polite, and the word 예 is formal polite. There's a quickly difference of these two, and they have to be used in different ocasions. Exemple: You can use 예 when the occasions are meetings, presentations, to talk to someone superior at work. And 네, you can use in daily conversations between friends, toward someone older/strange.