Is there a difference between qiyamul layl and tahajjud?

It is recorded in a narration of Tabrani that any Nafil Salaah performed after Esha Salaah will be termed as Salaatul-Layl or Qiyamul-Layl.

Whatever Salaah is performed after Salaatul Esha then it is from (Salaatul) Layl.

Tahajjud refers to that Salaah that is performed in the letter part of the night ideally after awakening from one’s sleep. There is a statement of Hajjaj bin Amr in Tabrani in regards to the definition of Tahajjud. He states:

Tahajjud is only that Salaah that is performed after awakening.

From the above, it can be gleaned and ascertained that yes, there is a difference between Qiyamul-Layl and Tahajjud in that the relation between the two is that of Aam-Khaas-Mutlaq. Qiyamul-Layl is Aam-Mutlaq meaning that it is a more general term that can encompass any Nafl Salaah performed after Isha Salaah until Subh Saadiq (including Tahajjud in the latter part of the night), whereas Tahajjud (being Khaas-Mutlaq), is the Nafl Salaah performed specifically in the latter part of the night (prior to Subh Saadiq preferably after having slept in the early part of the night) and it cannot be used to describe the Nafl Salaah performed in the early part of the night after Isha Salaah.