Is the intention for performing a prayer on time and for making up a missed prayer obligatory, and is the prayer invalidated by not distinguishing between the two?

Intention is a condition for the validity of prayer, and its place is the heart; uttering it verbally is an innovation (bid'ah). Its benefit lies in distinguishing acts of worship and distinguishing some from others. For obligatory prayers, the intention for the specific prayer (Dhuhr or Asr) is necessary. For designated supererogatory prayers (such as those for an eclipse, seeking rain, or Tarawih), specifying the intention is required. However, for absolute supererogatory prayers (like night prayers), intending prayer generally suffices. The preponderant opinion among most jurists is that the intention of obligatoriness, performance, making up (qada'), or repetition (i'adah) is not a condition for obligatory prayers; mere designation is sufficient.