What is the ruling on applying the terms "Qur'an" or "Mushaf" to something other than the Book of Allah?

There is no impediment to metaphorically applying the terms "Qur'an" or "Mus'haf" to things other than the Book of Allah, to denote perfection and precision. For instance, Al-A'mash was called "Al-Mus'haf" due to his truthfulness, and the phrase "as if it were a Mus'haf" is used to describe the precision of something. Sibawayh's book was described as "the Qur'an of grammar" due to the precision and uniqueness of its content.

Further support for this can be found in Aisha's (may Allah be pleased with her) description of the Prophet's (peace and blessings be upon him) character: "His character was the Qur'an."

As for the phrase "So-and-so's Mus'haf," scholars used it to refer to copies of the Qur'an that differed from Uthman's Mus'haf, such as "Umar's Mus'haf," "Ali's Mus'haf," and "Ubayy ibn Ka'b's Mus'haf." This does not mean that these were their own words, but rather what they heard from the Prophet (peace and blessings be upon him), or what was transcribed during the final review of the Qur'an.