Dungeons and Dragons – Is Eladrin Heavenly or Fairy?

In Wizards Presents: Worlds and Monsters, Matthew Sernett and James Wyatt explain how and why they redefined Eladrin for the 4th edition. At the time this book was written, the 4th edition had not been published yet (and, apparently, the plural of "eladrin" was "eladrin"):

In the 3rd edition of D & D, eladrines were a kind of celestial being conceived by dividing the "tart" of alignment between divine servants. The warrior archons were legally good, the animal-headed guardinals were good neutrals, and the eladrins received the good, chaotic part of the pie.

We knew we did not want to design monsters anymore based on this topic. Well-aligned creatures may be useful, but D & D simply does not need them. […] And since our cosmology no longer relied on the alignment-based concept of the Big Wheel, it was not necessary to create planar inhabitants for every imaginable alignment combination.

But even if the Big Wheel, its many outer planes and their different races were abandoned for the cosmology of the 4th edition, the eladrins were preserved (or reconverted), now become the "banner race" of the Feywild, rather than 39. Arborea – and exclusively fey creatures, rather than celestial:

As we discussed what to do with [eladrin]we noted their generally fairy-like appearance, which led to a natural association with the Feywild. […] The 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 the 5th edition saw another cosmological upheaval: the Feywild, a popular element of the 4th edition, was preserved, but the outer planes, including Arborea, returned to the default cosmology. However, the eladrin sub-race as presented in 5G DMG, Unearthed Arcana and finally the Tome of Foes of Mordenkainen are all "Feywild creatures" derived from version 4.

So, there are two versions of Eladrin, and the difference is only a matter of what edition you look at it: Before the 4th edition, Eladrin were Celestials of Arborea; from the 4th edition, they are fey creatures of Feywild.