Extra Language, Fey
Fey is a mostly dead language, since those who most commonly spoke it, are extinct.
Just as elves have fey ancestry, so does their language. Elvish originated as a dialect of fey.
The difference in speech between fey and elvish is much like the difference between UK English and US english, but slightly more pronounced (more like, the difference between Spanish and portugese). For the most part, one who was speaking fey to someone could speak elvish would more or less understand them. However, certain meanings may be lost in translation.