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I have a dumb question too. What is the difference between the Eldar and the Elves?
There is no difference as far as the beings are concerned in general, meaning the Eldar are Elves, and
Eldar is an Elvish word which can be translated by 'Elves'.
Elda 'Elf'
Eldar 'Elves'
however...... in Middle-earth there are many designations for these beings called 'Elves', and sometimes the meanings of a term can change.
Eldar referred to all Elves originally [The People of the Stars], but then it came to exclude the Avarin Elves. The Avari are still Elves but they are the Elves who refused the initial summons to travel West [across the Sea]. So Eldar now had a more narrowed application:
... 'the People of the Stars who took up the Great Journey into the West'.
to complicate matters more...... according to
The Lord of the Rings the Eldar were those Elves who journeyed West at least as far as Beleriand, including those who went even furter West across the Sea. Other Elves are 'East-elves' by comparison, so here the term
Eldar is basically equivalent to West-Elves.
But according to posthumously published descriptions, which includes the Silmarillion, the Eldar are those who took up this initial journey, no matter if they made it to Beleriand or not.
For me
The Lord of the Rings holds more weight, being published by the author himself, and going by this prime source only the Noldor and Sindar of Middle-earth are Eldar [plus the Vanyar of the Undying Lands].
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And what does half-elven mean?
Hmm,
in my opinion it refers to someone who has mixed blood, Elvish and mannish.
however...... it is not exactly clear to me when the term should or should not be applied with respect to meaure: for example, Tolkien refers to Arwen as half-elven and she was not specifically
'half' mortal and
'half' elven by blood. But on the other hand if some mortal had 'mostly' mortal blood but had an Elvish ancestor, we don't seem to find the term 'half-elven' applied to them.
Then there is the 'Choice of the Half-elven', which however appears to be special dispensation to only certain of the Half-elven -- as only Earendil, Elwing, Elros, Elrond, and Elrond's children, get the Choice.
So, not dumb questions at all, but complicated in some respects; in my opinion anyway