@Shuaibh and @mohd ali 99, Qiyaam al-layl means spending the night, or part of it, even if it is only one hour, in prayer, reading Qur’aan, remembering Allah (dhikr) and other acts of worship. It is not stipulated that it should take up most of the night.
Tahajjud means specifically praying at night, and some scholars limited it to prayers that are offered at night after sleeping.
qiyaam al-layl is more general than tahajjud, because it includes prayer and other actions, and it includes prayer before and after sleeping.

Tahajjud is exclusively praying, and there are two opinions concerning it. The first is that it means praying at any time of the night, which is the view of the majority of fuqaha’