1- What is the difference between the Salat at-Taraweeh, Salat al-Qiyam, Salat al-Lail and Salat al-Tahajjud? Explain me also these Salat in light of Ramadhan.
2- According to Sunnah of the Prophet, What is the actual Rakahs for the Taraweeh prayer? Usually, 90% of people including me praying 20 Rakahs, but 10% pray 8 Rakahs only, what's this? And in Makkah, they lead 20 Rakahs. Please explain briefly, as I am a new Muslim.

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, sallallaahu 'alayhi wa sallam, is His slave and Messenger.

The night prayer is any voluntary prayer performed at night, i.e. between ‘Isha’ prayer and Fajr prayer. So, At-Taraweeh, At-Tahajjud and Al-Qiyyam all refer to the night prayer. At-Tahajjud is the prayer performed after having slept and then one wakes up especially for the prayer, and this is also called Nashiatul-Layl. ‘Aa’ishah, may Allaah be pleased with her, said: “An- Nashia (At-Tahajjud) is the one that is performed after waking up by night”. The night prayer is a confirmed Sunnah. But it is more confirmed during Ramadan as the Prophet said: “Whoever prays during the nights of Ramadan [Taraweeh] with a firm belief and hoping for the reward from Allah, all his previous sins will be forgiven.”

Praying Taraweeh prayers just after ‘Isha’ or at a later time is considered as Qiyyam in Ramadan. But it is better to delay the Taraweeh until the last third of the night –if this is not difficult for the congregation –as 'Abdur-Rahman Ibn 'Abdul-Qari said: "One night during Ramadan, I went with 'Umar to the mosque and the people were praying in different groups. Some were praying by themselves and others were praying in small groups. 'Umar said: 'I think it would be better if I gathered them under one Imam.” Then he did so and appointed Ubayy ibn Ka'b, may Allaah be pleased with him, as the leader of the prayer. Then I went out with him on another night and all the people were praying behind one Imam and 'Umar said: “What a good innovation this is”, but it is better to sleep and delay it until the last part of the night." 'Umar remarked, the prayer which they do not perform, but sleep at its time is better than the one they are offering.” [Al-Bukhari] He meant the prayer in the last part of the night. (In those days) people used to pray in the early part of the night.”

As for the number of Rak’ahs in Taraweeh prayer, please refer to Fataawa 82507 and 82508.

Allah knows best.