Islam in the Ottoman Empire
Islam was the official religion of the Ottoman Empire. The highest position in Islam, "caliphate", was claimed by the sultan, after the defeat of the Mamluks which was established as Ottoman Caliphate. The Sultan was to be a devout Muslim and was given the literal authority of the Caliph. Additionally, Sunni clerics had tremendous influence over government and their authority was central to the regulation of the economy. Despite all this, the Sultan also had a right to decree, enforcing a code called Kanun (law) in Turkish. Additionally, there was a supreme clerical position called the Sheykhulislam ("Sheykh of Islam" in Arabic). Minorities, particularly Christians and Jews but also some others, were mandated to pay the jizya, the poll tax as mandated by traditional Islam.
Ottomanism
Ottomanism was strongly influenced by thinkers such as Montesquieu and Rousseau and the French Revolution. It promoted equality among the "millet"s. The idea originated amongst the Young Ottomans in areas such as the acceptance of all separate ethnicities in the Empire regardless of their religion, i.e. they were all 'Ottomans' with equal rights. Put simply, Ottomanism stated that all subjects were equal before the law. Ideally, all citizens would share a geographical area, a language, culture, and a sense of a 'non-Ottoman' party who were different than them. The essence of the "millet" system was not dismantled, but secular organizations and policies were applied. Primary education, conscription, head tax and military service were to be applied to non-Muslims and Muslims alike.