"Mezmur" is a term most commonly used by Ethiopian Orthodox Christians. "Mezmur" literally means "music" in Amharic, the language of Ethiopia, so it is in common usage not just among Ethiopian Orthodox people, but among all Ethiopians.
The Ethiopian Orthodox branch of Christianity is not affiliated with the Eastern Orthodox Church that predominates in Greece and Eastern Europe. Ethiopian Orthodox and other Coptic Christian churches split off from what is now the Catholic Church long before their Greek counterparts. The Ethiopian Orthodox Church is one of the few pre-colonial churches in Africa, having been established as the official religion of Ethiopia in the fourth century A.D.