The Noldor returned to Middle-earth as the Moon and Sun first rose; many returned in to the West at the end of the First Age, but others remained to the end of the Third Age and even beyond
A phrase used to describe the Noldor in Middle-earth, after they returned out of the Uttermost West to make war on Morgoth. It would seem reasonable to assume that 'Elves of the West' could also be used to describe those Eldar who had remained in Aman, but in practice it is only ever used to refer to those Elves who had travelled back to Middle-earth.
Notes
1
In a broad sense, the phrase 'Elves of the West' might be taken as referring to all the Elves who dwelt in Aman, and in that sense it would be identical in meaning to names like 'Elves of Valinor' and its equivalents. All our recorded instances of its use, however, refer to Elves in Middle-earth; that is, Elves who came out of the West rather than Elvesin the West. It is in this narrower sense that the name is discussed here.