It is to be noticed that, Taraweeh prayers has been called (قيام ضهر رمضان) Kiyamu Shahre Ramadan, (قيام لليل) Kiyamul Lail etc in the Hadeeth shareef. For example it has been mentioned that
قال الكرمانى- اتفقوا على ان المراد بقيام رسمضان
التراويح- وبه جزم النووى وغيره (اوجزالمسالك)
Meaning: Allama Kirmani Rwa’hmatullahi ‘Alaihi says, everyone is unanimous that, “Qiyamu Rwamadwan” points at the Taraweeh Swalaat. This is the opinion of Imaam Nababi Rwa’hmatullahi ‘Alaihi and everyone else.
وفى الاقناع- اتفقوا على ان التراويح هى المراد من قوله صلى الله عليه وسلم قام رمضان وفى شرح الكبير- التراريح هى قيام رمضان.
Meaning:- It has been mentioned in the book Al Iqna, everyone has agreed that by the hadeeth قام رمضان talks about Taraweeh prayer. And in ‘Sharhul Kabir’ Taraweeh is called ‘Quiyamu Ramadan.’ Therefore it is proven that wherever قام رمضان Qiyamu Ramadan has been mentioned, it means Taraweeh prayer. And even though ‘Qiyamul Lail’ (قيام لليل) being Taraweeh is debated; most Muslims agree that it means Taraweeh prayer. It has been mentioned in scriptures regarding this,
“Maximum Muhaddis have talked about Taraweeh prayer when they say ‘Quiyamul Lail’ (Ahsanul Fatwa, also mentioned in Hedaya, Fathul Qadir, Mabsut and Badayet.)
Apart from that, it has been mentioned in the Hadeeth shareef that, جعل الله صيامه قريضة وقيام ليله تطوع- (بيهقى شريف
Meaning:- ‘Allah paak the greatest has made fasting in rozas mandatory for you and ‘‘Quiyamul Lail’’ or night prayer (Taraweeh) Nafl (Sunnate Muakkadah)’ (Baihakki Shareef)
Mainly: Taraweeh prayer has been called ‘‘Quiyamul Lail’’(قيام لليل) in the above mentioned Hadeeth shareef. Therefore, Quiyamul Ramadan قيام رمضان and Quiyamul Lail (قيام لليل) are terms used to define Taraweeh prayer.