The Eldar: Once, all elves were called Eldar, eventually this name was given to three groups of western elves who answered the summons of the Valar. The first elves awoke on three groups, their leaders were Imin, Tata, and Enel.
The Avari: “Dark Elves” or “The Refusers” those of whom refused the summons to Aman, staying East of the Misty Mountains. Comprised of half of the Noldor (Tatyar) and almost half of the Teleri (Nelyar).
From the Eldar there were three groups:
Vanyar - “Fair Elves” Golden-haired descendants of Imin, led by the High King Ingwe, all of them completed the Great Journey to Aman.
Noldor - “Deep Elves” Dark-haired descendants of Tata, led by the King Finwe, half of which completed the Great Journey to Aman. (Also known sometimes as Gnomes in older manuscripts)
Teleri - “Sea Elves” or “The Singers” Silver-haired descendants of Enel, led by the King Olwe, a little over half completed the Great Journey to Aman (this group specifically is called the Falmari).
From the Teleri, two groups of Elves descended:
Sindar: “Grey Elves”, kin of Elwe-brother of Olwe (also called Elu Thingol), a Teleri, who remained in Doriath of Beleriand after meeting the Maia Melian.
Nandor: “Those who go back” kin of Lenwe, a Teleri, who led his people to the Vales of the Anduin.
From the Nandor, two groups of Elves descended
Silvan: “Wood Elves”, descendants of the Nandor, most of whom remained east of the Misty Mountains.
Laiquendi (Laegrim): “Green Elves” kin of Denethor, son of Lenwe, most of whom lived west of the Misty Mountains in Ossiriand and Lindon (those in Lindon became the Falathrim, sea-loving sailors and shipwrights led by Cirdan).
I take issue with your definition for the Avari Elves. My own understand is that all Elves who started out on the Great Journey to Aman are counted among the Eldar regardless of whether they finished it. The Avari, or East-elves, were those Elves who never set out on the Great Journey at all.
Also, Silvan Elves (Wood-elves) are a mixture of both Nandor who settled east of the Misty Mountains and Avari who came to dwell in the Greenwood and Lothlórien in the years after the Great Journey.
Well there are the following:
There is a video about them on YouTube😉
Also, the fair-haired Vanyar who remained in Valinor (though they took part in the War of Wrath that ended the First Age).
I forgot about the Vanyar🤔