The Greatest of the Eldar

[Galin]

Another way to view the distinction might not be so much with respect to the West Lands of Middle-earth of Frodo's day, but rather the West as in Over Sea plus Beleriand. And the Sindar (in general at least) had reached about as West as you could go without sailing Oversea. Note, from the Lhammas again (but just for comparison):

'This is very clear. The term Eldar has acquired its later significance of the Elves of the Great Journey (only), and is not restricted to those who in the end went to Valinor, but includes the Elves of Beleriand: the Eldar are those who completed the journey from Kuiviénen to the country between Eredlindon and the Sea.'

This seems a model for the later Eldar 'West-elves'.

'On the other hand all Elves who did depart from Kuiviénen but who did not complete that journey are numbered among the Lembi. The term Ilkorindi is now used in a much narrower sense than previously: specifically the Eldar of Beleriand -- the later Sindar, or Grey Elves.'

In Lhammas A the Eldar are the departed, including those that went to Valinor and those that reached Beleriand but remained there -- while the Lembi includes those that remained in the East and those that were lost on the journey to Beleriand. This seems an early model for East-elves, though revision was to follow of course.

If 'the Elves far back in the Elder Days became divided into two main branches' the movements of the Nandor spreading into Eriador, and finally entering Beleriand may not have changed the fact that they essentially were considered East-elves. For example, even entering Beleriand 'somewhat later' might have carried a distinction in the minds of the Sindar: 'Moerbin was similarly an equivalent for Avari; but that it did not mean only 'Dark-elves' is seen by its ready application to other Incarnates, when they later became known. By the Sindar anyone dwelling outside Beleriand, or entering their realm from outside, was called a Morben.' Q&E