The interchange of the terms "elf" and "fairy" and the resulting confusion is something of a convoluted story.
The simple version: both can be referred to in Japanese by the word yousei (which also refer to sprites too). This grouping-together has never been true in modern English pop culture, where "fairies" were tiny winged females out of Disney movies and "elves" were cultivated by the popularity of J. R. R. Tolkien's works into the "long-lived, high-class" image they have today. As Japanese generally use the loanword erufu to specify the version of elves that stems from Tolkien, and both Chydis and Olivie refer to themselves as erufu, the "fairy" part of the localization can be chalked up to mistranslation.
The version accounting for history: in folklore, "fairy" was the label attached to magical creatures of all sorts of varying shapes and sizes and power, which included the older kind of elves (think of Santa's Little Elves and the Harry Potter series' "house-elves"), pixies, dwarves (which we'll get in Aigis later), undines, trolls, sometimes goblins and gnomes. However, these creatures were only loosely connected to each other, and even then only by the label of "fairy"/"faerie", the adjective form of "fae"/"fay"/"fey", all of which has literal meanings that can be summed up as "with magic". Time marched on, and the stories of the various fairies were edited to be more child-friendly (like taking out the bit where they tended to seduce people). By the modern day, they turned into versions of themselves removed from what they once had been. As a result, much like several related people who all share the same grandparents but who all have different surnames, "fairy" used in the older sense of the word is one way to refer to the whole family, but it's not immediately apparent whether you're referring to that one cousin who still has that same surname, or you're referring to the whole group of people whose parents used to have that last name. You probably wouldn't even know in the first place they were related unless you're told or you're already in the know.
Also, from an in-game perspective, using "fairy" in its older meaning could bring up the question of whether demons would also be considered "fairies".
In conclusion, it probably would've been better if they acknowledged pop culture and used one of the related word less charged with meaning in the modern era. I'd go with "the Fae". -
You must be registered to see the links
Some sources:
-
You must be registered to see the links
article on TvTropes
-
You must be registered to see the links
and
You must be registered to see the links
articles on Wikipedia (bit of a tough
reading, though)