I can answer with the Arab part (Mamluks). It started with the Abbasids, who came to power after revolting against the Umayyads. The Abbasids recruited non-Arab slaves as personal elite guard, since they did not have any affiliations to any Arab tribe and their loyalty would be only to the King/Caliph, and so they would not replicate what they did to the Umayyads and lead a revolt. ِAnother reason which is attributed to Al-Mutasim (833 AD) that he recruited exclusively Turkish mamluks because he feared that freemen would be ambitious to make a coup, or that they would be fanatic about fighting their own clans or clans allied to them in the case of Arabian soldiers. With time they grew in numbers and power and by the time of Al-Mutawakkil (861 AD) there were nearly 15,000 Mamluks in Samaraa, they were the highest ranking officials of the state, with these regional Mamluk generals controlling smaller states split from the Caliphate like The Tulunids, The Ikhshidids, The Safarids, The Seljuks, The Ayyubids etc. The Ottomans kept this tradition of recruiting foreign slaves as military elites, but since they were Turkish they recruited Greeks, Slavs, and other Eastern Europeans as Janissaries. As for the Byzantines I don't really know, but my guess is that they borrowed the concept from their Turkish neighbours?