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 at least 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.