I’m assuming this is because of the Elvish Cross-Cultural Relation series that I’ve been posting, right? (If you haven’t yet, check them out here.) If so, it’s no wonder, because I really didn’t explain it well, lol.
For all intents and purposes, the Minyar, Tatyar, and Nelyar are synonymous with Vanyar, Noldor, and Teleri. (To clarify: Minyar=Vanyar, Tatyar=Noldor, Nelyar=Teleri.) And, in fact, on this blog I’ve never even brought up the older names because the distinction is so minute that it just hasn’t been worth it to explain before.
When the elves first awoke, they immediately split into three tribes. These tribes were called the Minyar (Firsts), Tatyar (Seconds), and Nelyar (Thirds.) Then, after meeting the Valar and being invited to Valinor, a fourth split occurred. Those elves who wanted to stay in Middle Earth became known as the Avari, and left the original three tribes.
After this split (called the Sundering of the Elves), the original three tribes took on knew names, to signify their new identities without their Avarin kin. The Minyar became known as the Vanyar (meaning “the Fair”), the Tatyar became known as the Noldor (generally meaning “the Wise”), and the Nelyar became known as the Teleri (meaning “the Lasts.)
Anyway, like I said, unless you’re really looking at the gritty details of early elvish society or cross-cultural relations, it isn’t all that important to know about the Minyar, Tatyar, and Nelyar. It’s far easier to stick with the much more well known - and nearly synonymous - Vanyar, Noldor, and Teleri.
(And as for the six tribes of the Avari, we literally don’t know anything about them other than their names, which I listed in the Avarin Relations post.)
Hope this helped!
SOURCES: Histories of Middle Earth vol. 11 (“Quendi and Eldar”)