Praise be to Allah.
Salaat al-Taraaweeh is classified as part of qiyaam al-layl; they are not two different prayers, as many people think. Qiyaam al-layl during Ramadaan is called Taraaweeh because the salaf or early generations of Islam (may Allaah have mercy on them) used to rest (istaraahu) after every two or four rak’ahs, because they made their prayers long in order to make the most of this season of great reward. They were eager to earn the reward mentioned in the hadeeth: “Whoever stays up and prays at night in Ramadaan out of faith and in the hope of reward, all his previous sins will be forgiven.”
(Reported by al-Bukhaari, no. 36). And Allaah knows best.