Byzantine is anything pertaining to the Byzantium Empire or its period of existence. Islamic are those things relative to the religion of Islam.
The Byzantine Empire had a Roman culture and Orthodox Christianity as its state religion. The Islamic Caliphates had Arab culture and Sunni Islam as their state religion.
One is bigger than the other one.
There was hardly any similarity between the Byzantine and the Islamic world. Moreover, the Byzantines were orthodox Christians. However, the Byzantines there was a degree of influence of the Greek classics of the Arabs. The Arabs took over Syria, Lebanon, Palestine and Egypt, which belonged to the Byzantine Empire. The Arabs became interested in Greek learning and science. The Byzantine domes also influenced Arab dome construction.
How were lands that were once part of the Byzantine Empire added to the Islamic world?
Invasions by the Islamic Ottoman Empire destroyed the Byzantine Empire.
Much was preserved by the Islamic medieval Islamic scholars.
In what ways were the Byzantine and Islamic civilizations different from the civilization developing in western Europe?
yes
Through Trade and Conquest.
Byzantine culture influenced a lot of Islamic architecture especially the dome shape that many Mosque have.
The Byzantine Empire.
In both the Islamic and Byzantine world, women are or were treated in several ways. They were revered for their ability to create life, subjected to punishment for their inability to remain silent regarding family values, and suppressed in their intellectual pursuits.
The Roman rite comes from the diocese of Rome, and is different from the Byzantine Rite, which comes from the diocese in Byzantium, in the ways it celebrates its masses and decorates its churches.
Invasions by the Islamic Ottoman Empire destroyed the Byzantine Empire.