What is the difference between Taraweeh prayer and Tahajjud prayer, and what is the number of rak'ahs for each of them?

There is no difference between Tarawih, Qiyam, and Tahajjud prayers; all are voluntary prayers performed between Isha and Fajr. Tahajjud is more specific, performed after sleep in the last third of the night, and it is superior. The number of rak'ahs in Tarawih and Tahajjud is the same.