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.