In every meaningful way, the Byzantine Empire and the Islamic Empire were fundamentally different. On the most surface level, there is the obvious distinction between the dominant religions of the two groups. The Byzantines were Christian and the Islamic empires, whether the Umayyads, Abbasids, or Ottomans, were of course Muslim. Conflicts over land rights and other issues kept the two groups in opposition for many years. However, despite the conflicts, Byzantine and Islamic empires not only had similar cultural moments but also were viewed in similar ways by the people of Western Europe, who saw them both as outsiders.
The Byzantine Empire was the successor to the Roman Empire, and built on the principles of Christianity, only centered in the east in Constantinople with territorial holdings in Asia Minor, Eastern Europe, and the Middle East. Islam, meanwhile, rose out of the Arabian Peninsula in the 7th century and rapidly challenged the Byzantine Empire through a series of various empires, including the Umayyads, Abbasids, Seljuks, and Ottomans.
On the surface, the Byzantine and various Islamic empires were fundamentally opposed and almost consistently engaged in warfare. This warfare began in the 7th century when the new Islamic empires conquered Byzantine provinces in Africa and Asia and threatened Constantinople itself, and continued on and off until the 11th century when a new regional power, the Seljuks, threatened Byzantium. Though the Crusades helped the Byzantines reclaim some of their lost territory, the Ottoman Turks would eventually conquer Constantinople in 1453.
Despite the warfare, Byzantine and Islamic cultures had moments of similarity. Islam is a famously iconoclastic religion, meaning it bans all icons, or images, of religious figures such as its Prophet Muhammad, fearing that they lead to idol-worship. The Byzantine Empire in the 8th century underwent an iconoclast period, motivated in part by Islamic iconoclast culture. Emperor Leo III ordered the destruction of religious icons, many of which were glorious pieces of Byzantine art.
View from Europe
The Western Church in Rome viewed this iconoclasm as undue Islamic influence on the Byzantines, and thus it contributed to their view of the Byzantines and Muslims as equally foreign. By the 11th century the Eastern and Western churches had split, and Constantinople was viewed by the Latin West as a foreign power with a foreign religion. Western Europeans not only invaded Constantinople during the Fourth Crusade of 1204, but they also offered little assistance when Constantinople was later besieged by the Turkish armies in 1453.