Who are the Tabi'un? And who are the Atba' al-Tabi'in?

The Tabi'un are those who met a Companion and died as Muslims, and the Atba' al-Tabi'in are those who met a Tabi'i but did not meet any Companion. Al-Bukhari and Muslim reported from Ibn Mas'ud that the Prophet, peace and blessings be upon him, said: "The best of people are my generation, then those who follow them, then those who follow them." The first generation referred to are the Companions, the second are the Tabi'un, and the third are the Atba' al-Tabi'in. After them, falsehood spread and innovations appeared.