The Elves spoke a single language when they awoke at Cuiviénen. Over time, the dialects of the Elves drifted and became separate languages like Sindarin and Quenya, and their original language was forgotten. Some of that original language can be reconstructed by comparing the Elvish languages that developed from it, in much the same way that ancient human languages can be deduced by comparing modern languages.
In Tolkien’s writing, he distinguished two phases of development for Primitive Elvish: Primitive Quenderin and Common Eldarin. Primitive Quenderin (also called Common Quenderin) was the language as it was spoken at Cuiviénen, while Common Eldarin was the form of the language spoken by the Eldar as they marched to Aman, distinct from the languages of the Avari (PE18/72). Since very little is known of the Avari languages, it can be difficult to determine which linguistic features developed in the Common Eldarin phase and which belong to Primitive Quenderin. For simplicity, this lexicon groups both phases of development under “Primitive Elvish”.