Christian Sects:-

       At the time of Muhammad, the Arabian Christian tribes belonged to different warring sects. Their written and spoken language was Syriac, a western dialect of Aramaic.

1        Jacobite/Monophysite: belief that there is only ONE inseparable nature (partly divine and partly subordinate human) in the person of Jesus. They were the dominant party in the kingdom of Ghassan   

       The Monophysites spoke of him as one person (hypostasis) and one  nature (physis), both God and man.

2        Nestorian: The Christian doctrine that there are TWO separate persons, one human and one divine, in the incarnate Christ.   

        Nestorius spoke of Christ as one person (prosopon) in two natures (physis), human and divine.

3        Melkite: Orthodox or Uniate Christianity belonging to the patriarchate of Antioch, Jerusalem or Alexandria (from Syriac, Malkaya meaning Royalist); agreeing with the Byzantine emperor. 

        So Melkites are the present day Catholics who follow the Byzantine worship, theology, and spirituality whose tradition is in the Middle East.