Tahajjud is a great recommended worship for every night of the whole year. It is also called Salat Al-Layl or Namaz Shab. It is performed individually and not with congregation. Umar Ibn al-Khattab ordered during his government to pray Tahajjud with congregation which was then called Taraweeh.
Taraweeh is a Bid'ah which was never practiced by the Prophet Muhammad (SAWA) but was initiated by Omar Ibn al-Khattab in year 14 after Hijra.