Are eladrin celestial or fey?

Question

This question was sparked by looking into the lore about eladrin after reading the comments under this question.

According to this wiki page,

Celestial eladrin [...] were fey celestials native to Arborea

According to the playable race in Unearthed Arcana: Eladrin and Gith (September 2017):

Eladrin are elves native to the Feywild, a realm of unpredictability and boundless magic. At your DM’s option, you can select eladrin as the subrace for an elf character, instead of one of the elf subraces in the Player’s Handbook.

Or more recently in Mordenkainen's Tome of Foes p. 61 they were

elves native to the Feywild, a realm of beauty, unpredictable emotion, and boundless magic.

Are these three races separate or the same? If they're not the same then how do you tell the difference in published content?

Answer 1

In Wizards Presents: Worlds and Monsters, Matthew Sernett and James Wyatt explain how and why they redefined eladrin for 4th Edition. At the time when this book was written, 4th Edition had yet to be released (and, apparently, the plural of "eladrin" was "eladrins"):

In 3rd Edition D&D, eladrins were a kind of celestial being designed by dividing up the alignment “pie” among divine servants. The warrior archons were lawful good, the animal-headed guardinals were neutral good, and eladrins got the chaotic good slice of the pie.

We knew that we no longer wanted to design monsters according to that rubric. Good-aligned creatures can be useful, but D&D simply doesn’t need that many of them. [...] Also, since our cosmology no longer hinged upon the alignment-based concept of the Great Wheel, we didn’t need to create planar inhabitants for every conceivable alignment combination.

But even though the Great Wheel, its many Outer Planes, and their various races were scrapped for 4th Edition's cosmology, the eladrin were preserved (or retconned)—now as the "banner race" for the Feywild, rather than Arborea—and as exclusively fey creatures, rather than celestials:

As we discussed what to do with [eladrin], we noted their generally fey appearance, and this led to a natural association with the Feywild. [...] Eladrins were already powerful magical beings in previous editions of the game. Now they have a very similar role, but as mysterious lords and ladies of the Feywild.

The advent of 5th Edition saw another cosmological shakeup: The Feywild, a popular element of 4th Edition, was preserved, but the Outer Planes, including Arborea, returned to the default cosmology. However, the eladrin subrace as presented in the 5E DMG, Unearthed Arcana, and finally Mordenkainen's Tome of Foes are all "creatures of the Feywild" derived from the 4th edition version.

So there are two versions of eladrin, and the difference is only a matter of what edition you're looking at: Before 4th Edition, eladrin were celestials from Arborea; beginning with 4th Edition, they're fey creatures from the Feywild.

Answer 2

In 5e, eladrin player characters have the humanoid type - though all elves are descended from fey, and eladrin are native to the Feywild.

The celestial eladrin described in that wiki page are not from 5e; that wiki page exclusively cites sourcebooks from D&D 3.5e and earlier. The Forgotten Realms wiki in general reflects lore across all editions of D&D, not just D&D 5e.

In 5e, eladrin (Mordenkainen's Tome of Foes, p. 61-62) are a subrace of elves, which have the humanoid creature type (like all player races published so far except centaurs, which have a trait specifically classifying them as fey instead of humanoid).

This is true of every version of them in 5e - neither the UA version nor the version used in the DMG (p. 286) as an example of how to create a subrace have any racial trait specifying that their creature type is changed, as centaurs do.

Though they are humanoids, all elves are descended from fey creatures, as suggested by their Fey Ancestry trait. In addition, as you quoted, the eladrin are closer to their fey ancestors than most, as they are native to the Feywild itself (rather than the Prime Material Plane).

Eladrin "monsters"/NPCs are fey.

Some keen-eyed people might note that Mordenkainen's Tome of Foes also contains 4 monster statblocks for eladrin (p. 195-197): autumn, spring, summer, and winter eladrin. These monsters have the fey creature type, rather than humanoid.

Jeremy Crawford clarifies here that this difference is intentional:

Do eladrin player characters count as fey like they do in MToF for spells like Detect/Dispel/Protection from Evil and Good?

Playable elves are humanoid. Some of their kin are fey.

The playable eladrin in "Mordenkainen's Tome of Foes" are an elf subrace and are therefore humanoid. If they had a different creature type, they would have a trait that said so.

He elaborates further on elves, the fey, and the Feywild in a series of tweets here.