From an English perspective (i.e., how these words are used in everyday conversation), a juice is a drink made from fruits and vegetables, while a nectar is a more-seldom-used word that might be used to refer to a beverage that is sweeter, thicker, or pulpier than a juice – particularly if it's made from a more exotic fruit.
Things get trickier when you are talking about using the terms from a scientific, legal, or labeling perspective. There are many columns on the internet talking about the technical differences between these two terms – as an exercise for the learner, simply type "difference between juice and nectar" into your favorite search engine, and you'll find many columns (like this one) from juice companies and nutrition experts trying to explain the dividing line, which is as fuzzy as a ripe peach.
In everyday conversation, though, I wouldn't expect anyone to come to my house and ask for a glass of nectar; "Could I have a glass of juice?" is a question I am much more likely to hear. Even if the only carafe in my fridge was labeled "Apricot Nectar," I'd probably just pour that into a glass for my friend, and there's a good chance I would not even mention the slight deviation from the original request.