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.

Examples
 Qari Abdul Basit
 Qari Minshawi

These Qaris have memorized the whole Quran. Hafiz means a Muslim who memorized the whole Quran.

 References