Did Qadi Iyad, by his statement "sabahuma" (both of them), mean that the Mushaf is other than the Qur'an, or that the terms Mushaf and Qur'an are synonymous among scholars, and does doubt concerning a letter refer to the Qur'an or the Mushaf?

The Mus'haf (codex) is the book that collects the leaves of the Noble Qur'an. It acquired its sanctity due to the presence of the letters of the Qur'an within it, which is why the majority of scholars prohibit someone in a state of minor ritual impurity (al-muḥdith) from touching it. As for the Qur'an, it is the divine revelation sent down to the Prophet, peace and blessings be upon him, and the term Qur'an is applied to it whether it is recited or written. The term Qur'an may also refer to what is contained within the Mus'haf, as in the Almighty's saying: "Indeed, it is a noble Qur'an in a well-protected Book which none shall touch except the purified a revelation from the Lord of the worlds." (Qur'an 56:77-80). Whoever insults the recited or written Qur'an, or doubts a single letter of it, is considered a disbeliever if the conditions for excommunication are met.