What is the difference between a Tabi'i, a Tabi' al-Tabi'i, and a great, a middle, and a minor Tabi'i, in terms of time, duration, and the most famous figures?

A Tabi'i is one who met a Companion (Sahabi), and a Tabi' al-Tabi'i is one who met a Tabi'i. There has been a difference of opinion regarding the classification of the Tabi'in into layers (tabaqat); some made them three, while others said four, and some fifteen layers. The era of the Tabi'in is known to be from one hundred years to approximately seventy [Hijri], and the era of the Followers of the Tabi'in (Atba' al-Tabi'in) is from then until approximately two hundred and twenty [Hijri]. A layer (tabaqah) refers to a group of people who are close in age and who shared in receiving knowledge from the same شيخ (teachers/elders).