Is Witr and Tahajjud the Same?
Question

Is there a difference between Witr prayer and the night prayer?
Praise be to Allah.The Witr prayer is part of the night prayer, but there is still a difference between them.
Shaykh Ibn Baz (may Allah have mercy on him) said: 
“Witr is part of the night prayer, and it is Sunnah and it is the end of the night prayer, one Rak`ah with which one concludes the night prayers at the end of the night, or in the middle of the night, or at the beginning of the night after ‘Isha’ prayer. You pray whatever you can, then you conclude it with one Rak`ah.” (Fatawa Ibn Baz, 11/309)
Shaykh Ibn`Uthaymin (may Allah have mercy on him) said: 
“The Sunnah – both in word and in deed – distinguishes between the night prayers and Witr prayer . The scholars also distinguished between them with regard to the ruling and the way in which they are done. 
How the Sunnah distinguishes between night prayers and Witr 
With regard to differentiation made in the Sunnah, according to the Hadith of Ibn ‘Umar (may Allah be pleased with him), a man asked the Prophet (peace and blessings of Allah be upon him): How are the night prayers done ? He said: “Two by two, then when you fear that dawn is about to break, pray Witr with one Rak`ah.” (Narrated by Al-Bukhari. See Al-Fat-h, 3/20) 
How the Prophet differentiated between night prayers and Witr
With regard to the way in which the Prophet (peace and blessings of Allah be upon him) differentiated between them in his actions, according to the Hadith of `Aishah (may Allah be pleased with her): The Prophet (peace and blessings of Allah be upon him) used to pray when I was lying down across his bed. When he wanted to pray Witr, he would wake me up and I would pray Witr. (Narrated by Al-Bukhari. See Al-Fat-h, 2/487). It was also narrated by Muslim (1/51) with the wording: “He used to offer his prayers at night when I was lying in front of him.” Then when only Witr was left, he would wake her up and she would pray Witr. 
Muslim also narrated (1/508) that she  (may Allah be pleased with her) said: The Messenger of Allah (peace and blessings of Allah be upon him) used to pray thirteen Rak`ahs at night , five of which were Witr, in which he would not sit except at the end. And he narrated from her (1/513) that when Sa’d ibn Hisham said to her: “Tell me about the Witr of the Messenger of Allah (peace and blessings of Allah be upon him),” she said: “The Prophet (peace and blessings of Allah be upon him) used to pray nine rak`ahs during which he would not sit except in the eighth Rak`ah, when he would remember Allah and praise Him and call upon Him, then he would get up without saying the salam, then he would stand and pray the ninth Rak`ah, then he would sit and remember Allah (Dhikr) and praise Him and call upon Him, then he would say a Taslim that we could hear.” 
How the scholars differentiated between the ruling on Witr and night prayers 
With regard to the way in which the scholars differentiated between the ruling on Witr and the night prayers , the scholars differed as to whether Witr is obligatory. Abu Hanifah was of the view that it is obligatory, and this was narrated from Ahmad in Al-Insaf and Al-Furu`. Ahmad said: Whoever fails to pray Witr deliberately is a bad man whose testimony should not be accepted. 
The well known view in our madhhab is that Witr is Sunnah. This is the view of Malik and Al-Shafi`i. 
With regard to the night prayers, there is no such scholarly dispute. In Fat-h Al-Bari (3/27) it says: I have not seen anyone narrate the view that it is obligatory except for some of the Tabi’in. Ibn ‘Abd Al-Barr said: Some of the Tabi’in held an odd view and said that Qiyam Al-layl is obligatory, even if it is done only for the length of time that it takes to milk a sheep. But the view of the majority of scholars is that it is recommended. End quote. 
How the scholars differentiate between the ways in which Witr and night prayers are done
With regard to the scholars’ differentiating between the ways in which Witr and the night prayers are done, our Hanbali jurists have clearly stated that they are done differently. They said: The night prayers are done two by two, and they said concerning Witr: Witr may be prayed with five, or seven, Rak`ahs, in which one does not sit except in the last one. If a person prays Witr with nine Rak`ahs, he should sit immediately after the eighth Rak`ah and recite the tashahhud, then he should stand up before saying the salam and do the ninth Rak`ah, then he should say the tashahhud and the salam. This is what was stated by the author of Zad Al-Mustaqni`.” (Majmu` Fatawa Ibn `Uthaymin, 13/262-264) 
Thus it is clear that Witr prayer is part of the night prayers, but it differs from them in some minor details such as how it is done. 
And Allah knows best.