The science/study of how to correct & perfect one's pronunciation of the Quran, according to the original Arabic dialects that the Quran was revealed in. It focuses solely on the phonetics of the letter sounds & timing.

A "hafiz" is someone who has memorized the entire Quran in Arabic. In the old days, this term was used differently though, referring to scholars who'd memorized vast numbers of Hadiths, along with their chains of narrators and other pertinent details. In other words, when you hear about great scholars such as "Al-Hafiz Ibn Hajar al-'Asqalani", they were speaking about the giants and masters of the science of Hadith; it had nothing to do with the Quran. Back then, memorizing the Quran was just the beginning of one's journey in knowledge and becoming a scholar, often completed during childhood (i.e. like Elementary School).

A trained professional in the sciences of Quran recitation; someone who has mastered one or a few different Riwayat (canonical readings) of the Quran.

A trained professional in the sciences of Quran recitation, who has mastered most or all of the Riwayat (canonical readings) of the Quran.

The Maqamat are the melodic genres & patterns used in recitation. Learning how to use maqamat is an art that requires practice and time, and mastery generally requires training with a teacher.

The Qurān is defined as: the inimitable Word of God, the Book revealed in the Arabic language upon the heart of the Messenger of Allah - the Prophet Muhammad, peace & blessings be upon him. In order to be considered "The Quran", it must comprise all of the Surahs/chapters, from Al-Fatiha to Al-Nas. The Quran is that which has been mass-transmitted - the highest level of authenticity in the chains of narration - in every generation, from the present all the way back to the Angle Jibreel. And the Quran is a book that challenges its foes, even with its shortest chapter.

The word "Muṣḥaf" (plural "Maṣāḥif") however refers to a written or printed copy of the Quran. Therefore, it is incorrect for someone to refer to copies of the Quran as "Qurans", because that would appear to imply that there is more than one Book of God. Instead, one should try to use the term "Maṣāḥif" or a similar term.

Rasm refers to the science concerning the writing/spelling system of the Quran. It covers the letter shapes of the Quran, which essentially provide a skeletal framework by which the Quran is recited. Rasm is that which was divinely revealed to the Prophet, peace be upon him, through the Angel Jibreel.

Ḍabṭ is the science which complements Rasm, and covers how scholars utilize & add diacritic markings to the Quran in order to facilitate its recitation and memorization. This includes the dots & other marks added to the letters to distinguish those that share same-shape, the innovated shape of the Hamza, vowels, Sukoons, and more.