This is hard to answer. It's an old word, and not one which is used as often as it once was. Eldest, has an air of respect to it, it's also because the equivalent isn't as complimentary (especially in a woman's mind) , "oldest sister". She's the eldest. My eldest sister. Respect your elders. It basically means the oldest one, but it is more respectful and it's an old word. :) And in your title, "What's difference between ...." Don't forget "The" - "What's the difference between" - "the difference" - "the difference, IS"......... What is THE *? THE * is.............. The air, the difference, the problem, the solution, the day, the night, the man, the woman, to the end of time, always use "the". :)

Both have the same meaning, but you should use older sister. Elder sister sounds awkward to native speakers.