Short answer
Almost. Qiyam al-layl (standing at night) is any prayer you pray at night after Isha, including taraweeh and witr. Tahajjud is the night prayer you pray after waking from sleep. So all tahajjud is qiyam al-layl, but not all qiyam al-layl is tahajjud. Both are voluntary and greatly rewarded.
Night prayer after Isha is a sunnah (mustahabb) act with great reward, and tahajjud after sleep is its best form. It is prayed in sets of two, or four with one salam, with no fixed number. The Prophet ﷺ usually prayed eight rakats followed by witr.
The four schools agree on this.
Explanation
Qiyam al-layl literally means "standing at night". It covers any prayer between Isha and true dawn: voluntary rakats after Isha, taraweeh in Ramadan, witr, and the prayer of the last third of the night. Some scholars include other night worship such as reciting Quran and dhikr. Tahajjud is narrower: the night prayer after you have slept and woken. This is the meaning most scholars give, and it is the form the Quran praises when it speaks of those who forsake their beds.
The four schools agree that night prayer is voluntary, not obligatory, and that it is the best prayer after the fard. The Prophet ﷺ said exactly that, and he himself rarely left it. The Quran describes the believers as people who slept little of the night and asked forgiveness before dawn.
- How many rakats: no fixed number. Two is the minimum. The Prophet's ﷺ usual practice was eight rakats and then witr, and sometimes more or fewer.
- Best time: the last third of the night. See tahajjud time tonight.
- How: like any nafl prayer, in twos (or fours in the Hanafi school), reciting any surahs you know.
- In Ramadan: taraweeh is qiyam al-layl, and the Prophet ﷺ promised forgiveness for those who stand in Ramadan with faith and hope of reward.
For the step by step method, read how to pray tahajjud. For praying before sleeping see tahajjud without sleeping, and for Ramadan see how to pray taraweeh.
The evidence
Quran, Surah Adh-Dhaariyat 51:17-18
كَانُوا۟ قَلِيلًۭا مِّنَ ٱلَّيْلِ مَا يَهْجَعُونَ ﴿١٧﴾ وَبِٱلْأَسْحَارِ هُمْ يَسْتَغْفِرُونَ ﴿١٨﴾
They used to sleep but little of the night, And in the hours before dawn they would ask forgiveness,
Describes the righteous as people of night prayer and pre-dawn forgiveness.
Quran, Surah Al-Muzzammil 73:20
۞ إِنَّ رَبَّكَ يَعْلَمُ أَنَّكَ تَقُومُ أَدْنَىٰ مِن ثُلُثَىِ ٱلَّيْلِ وَنِصْفَهُۥ وَثُلُثَهُۥ وَطَآئِفَةٌۭ مِّنَ ٱلَّذِينَ مَعَكَ ۚ وَٱللَّهُ يُقَدِّرُ ٱلَّيْلَ وَٱلنَّهَارَ ۚ عَلِمَ أَن لَّن تُحْصُوهُ فَتَابَ عَلَيْكُمْ ۖ فَٱقْرَءُوا۟ مَا تَيَسَّرَ مِنَ ٱلْقُرْءَانِ ۚ عَلِمَ أَن سَيَكُونُ مِنكُم مَّرْضَىٰ ۙ وَءَاخَرُونَ يَضْرِبُونَ فِى ٱلْأَرْضِ يَبْتَغُونَ مِن فَضْلِ ٱللَّهِ ۙ وَءَاخَرُونَ يُقَٰتِلُونَ فِى سَبِيلِ ٱللَّهِ ۖ فَٱقْرَءُوا۟ مَا تَيَسَّرَ مِنْهُ ۚ وَأَقِيمُوا۟ ٱلصَّلَوٰةَ وَءَاتُوا۟ ٱلزَّكَوٰةَ وَأَقْرِضُوا۟ ٱللَّهَ قَرْضًا حَسَنًۭا ۚ وَمَا تُقَدِّمُوا۟ لِأَنفُسِكُم مِّنْ خَيْرٍۢ تَجِدُوهُ عِندَ ٱللَّهِ هُوَ خَيْرًۭا وَأَعْظَمَ أَجْرًۭا ۚ وَٱسْتَغْفِرُوا۟ ٱللَّهَ ۖ إِنَّ ٱللَّهَ غَفُورٌۭ رَّحِيمٌۢ ﴿٢٠﴾
Indeed, your Lord knows, [O Muhammad], that you stand [in prayer] almost two thirds of the night or half of it or a third of it, and [so do] a group of those with you. And Allah determines [the extent of] the night and the day. He has known that you [Muslims] will not be able to do it and has turned to you in forgiveness, so recite what is easy [for you] of the Qur'an. He has known that there will be among you those who are ill and others traveling throughout the land seeking [something] of the bounty of Allah and others fighting for the cause of Allah. So recite what is easy from it and establish prayer and give zakah and loan Allah a goodly loan. And whatever good you put forward for yourselves - you will find it with Allah. It is better and greater in reward. And seek forgiveness of Allah. Indeed, Allah is Forgiving and Merciful.
Shows the Prophet ﷺ and his Companions standing in prayer at night, and that Allah made it easy.
Sahih Muslim 1163
Sahih... أفضل الصلاة بعد الفريضة صلاة الليل ...
"The best prayer after the obligatory prayer is the prayer at night."
Shows the rank of qiyam al-layl.
Sahih al-Bukhari 37
Sahih... من قام رمضان إيمانا واحتسابا غفر له ما تقدم من ذنبه ...
"Whoever stands in prayer in Ramadan with faith and seeking reward will have his past sins forgiven."
Night prayer in Ramadan, including taraweeh, is a form of qiyam.
Where the ruling is recorded
- Radd al-Muhtar (Ibn Abidin), Kitab al-Salah, chapter on witr and nawafil. Night prayer is recommended; tahajjud in the proper sense is after sleep.
- Nur al-Idah with Maraqi al-Falah, Chapter on nawafil. Night prayer is among the recommended voluntary prayers.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.