What is the difference between the islamic empire and the byzantine empire (other then muslim and christian)?

Assuming you mean the Ottoman Empire, the Turks had a massively different mindset. The Byzantine were not religiously tolerant and they actively sought out the conversion of the Turks and other Muslim population. While the ottomans actively gave control of their own land to the Dhmiri a christian estate that payed moderate taxes for religious freedoms. Also the Byzantines had no African or Asian Ambitions like the Ottomans. The Greeks were more interested in Italy the anything else. The Ottomans on the other hand set up one of the largest transcontinental empire ever seen.