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When the Gnomes came to the Great Lands with Fëanor, they mixed and intermingled with the Ilkorindi, the Dark Elves; similarly their languages, Kornoldorin and Ilkorin were fused and amalgamated, this was the origin of Noldorin.
A celtic-sounding language spoken by the Gnomes/Noldoli existed since the beginning of Tolkien's mythology. In the first stage, it was called Gnomish quite similar to later Noldorin/Sindarin but also quite different.
Noldorin with all its backstory existed even while Tolkien was writing The Lord of the Rings. The Elvish phrases and languages, while nowadays are known as Sindarin, were "Noldorin" in Tolkien's mind while he was writing them. It was only while writing the Appendices when he decided to retcon all the backstory and give Elvish a new history and name, and then the language was standardized as Sindarin.
The Etymologies Noldorin is so similar and compatible to Sindarin, that Tolkien consulted it while working on Sindarin, by "updating" in his mind the old words with the new data. This methodology is used even now by Elvish students when they need to "import" or "update" Noldorin words into Sindarin proper. This practice is often referred to as "Neo-Sindarin", to distinguish it from attested Sindarin.
Example of differences
For example Old Noldorin initial l-/r- became lh-/rh- in Noldorin respectively, however they remain the same in Sindarin. Also, the Old Noldorin diphthong ai becomes oe in Noldorin but ae in Sindarin.
Therefore according to the Etymologies, the Old Noldorin word raika evolved into Noldorin rhoeg but the very same word should be "updated" into *raeg to become Sindarin.