What is the correct intention for voluntary prayers in the last third of the night? Is it sufficient to say, "voluntary prayer," or must one specify the intention of Tahajjud or Qiyam al-Layl, and what is the difference between them?

Witr prayer requires a specific intention, and a general intention for a supererogatory prayer is not sufficient for it. It is not obligatory to vocalize the intention; rather, it is disliked. If the worshiper has not yet prayed Witr, or is praying before Witr, a general intention for a supererogatory prayer is sufficient. Tahajjud is a supererogatory prayer performed after sleep, whereas Qiyam al-Layl (night prayer) includes what is performed both before and after sleep.