Qari

Qāri', or "reader", is a person who recites the Qur'an with the proper rules of recitation. 
Although it is encouraged, a reciter ("Qari") does not necessarily have to memorise the Qur'an, just to recite it with proper rules.
These Qaris have memorized the whole Quran. Hafiz means a Muslim who memorized the whole Quran.