Why do supplications in the Qur'an usually begin with "Our Lord" (Rabbana) and in the Sunnah with "O Allah" (Allahumma)?

The statement that the word "Allahumma" is not mentioned in the Quran is incorrect. It is mentioned in the Almighty's saying: "Said Jesus, the son of Mary, 'O Allah, our Lord, send down to us a table spread with food from the heaven'" and His saying: "And [recall] when they said, 'O Allah, if this is indeed the truth from You'". Furthermore, it is established in the Sunnah that the words "Rabbana" and "Allahumma Rabbana" appear in several supplications, including the Prophet's (peace be upon him) saying during bowing and prostration: "Exalted are You, O Allah, our Lord, and by Your praise. O Allah, forgive me," and his (peace be upon him) saying: "O Allah, our Lord, grant us in this world good and in the Hereafter good, and protect us from the punishment of the Fire."