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?
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"):
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:
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.