J.R.R. Tolkien uses Eldar primarily for the Elves who answered the summons to travel to Valinor.
In Tolkien’s legendarium, the Elves are the firstborn Children of Ilúvatar. The term Eldar originally referred to the Elves who undertook the Great Journey westward, although its use is tied especially to the peoples of Aman and their descendants. Elves who did not make that journey are generally called Avari.
This distinction is easy to blur because “Eldar” is sometimes used more broadly in discussions of Tolkien’s mythology. Elves also differ from Men in their immortality within the world, though they can be killed or grow weary. Their history includes the creation of the Silmarils and the wars against Morgoth.