Kiyam-ul-Layl:
Kiyam-ul-Layl is derived from the Arabic words "qama" and "layl," meaning to stand at night.
In a broader sense, it refers to any act of worship performed at night, including Salah, reading Quran, making Dua, etc.
Often, it is specifically used for night prayers.
Tahajjud:
Tahajjud is a specific type of Kiyam-ul-Layl, referring to the voluntary night prayer.
It is Salah performed at night, usually after sleeping, but not necessarily so.
Tahajjud is derived from the Arabic word "hajada," which means staying awake and sleeping alternately.
It is a voluntary night prayer that can be prayed after Isha and before the Fajr prayer.
And Allah knows best