In the Islamic society the leaders are the same in the Democratic state, president has been elected by the people in that society as normal way in the Democratic system we know in this days, also there is " Ahl Al-Zekr " they are bunch of men who has a great knowledge about the religion rules with no authority on the state, but they are there so the president can go back for advice from them.
The important leaders in the beginning of Islam are called Sahaba (Ashab-ı Kiram).
A person who saw Hadrat Muhammad at least once when he was alive, is called a 'Sahâbî'. It goes without saying that a Sahâbî is a Muslim. Ashâb is the plural form of Sahâbî. All the Sahâbîs are called 'Ashâb-i Kirâm'. If a Muslim has seen the Prophet, or talked to him, at least once when the Prophet was alive, he is called Sahabî. Plural form of Sahabî is Sahâba or As'hâb. The word Sahâba-i Kirâm includes all those great people each of whom has seen the Prophet at least once. The lowest of the Sahâba is much higher than the highest of other Muslims. If a person has not seen the Prophet but has seen or talked to one of the Sahâba at least once, he or she is called Tâbi'. Its plural form is Tâbi'în. In other words, the Tâbi'în are the successors of the Sahâba. If a person has not seen any of the Sahâba but has seen at least one of the Tabi'în, he or she is called Taba'î Tâbi'în. The Sahâba, the Tâbi'în and the Taba'i tabi'în altogether are called the Salaf-i Sâlihin (the early savants).
Sahâba were all (his Ashab) the companions of the Messenger of Allah 'sall-Allâhu 'alaihi WA sallam' and his Ahl-i-Bayt (his immediate relatives).
Hadrat Abû Bakr,Hadrat Umar, Hadrat Uthman,Hadrat Ali, 'radiy-Allâhu 'anhumâ', are the highest ones of the Ashâb-i-kirâm.
All religious authorities say in consensus that the Sahâba 'alaihim-ur-ridwân' are the third best and highest creatures after Prophets 'alaihimussalawâtu WA-t-taslîmât' and angels.
Refer to the links below for detailed information about Sahaba.
The early leaders of Islamic religion start by Adam, ..., Noah, ..., Abraham, ..., Moses, ..., Jesus, and Muhammad (peace be upon them all). All God prophets called their people to Islam that means full submission to God with no partner, no companion, no associate, and no equivalence.
Prophet Muhammad (peace be upon him) is the first leader in Islam per Quran revelation by God to prophet Muhammad through the angel Gabriel (or Jibril).
Prophet Muhammad (peace be upon him) is the first Islam leader.
There are many Islamic leaders who well recognized by Muslims as Religion knowing and understanding. There is no single person as for Catholics or Orthodox.
Abraham
It was the company of Walmart
Muhammad is said to be the founding leader and prophet of Islam
Prophet Muhammad (peace be upon him) is the original leader of Islam.
Mohammed, the final Islamic prophet was Islam's first leader.
Islam is a religion not a spiritual leader. Islam is not dead.
Islam daily leader is called Imam who leads Muslims on praying for God.
The leader of Islam is prophet Muhammad (peace be upon him) and started in Mecca (or Makkah) in Saudi Arabia.
The original leader of Islam religion per Quran revelation by God is prophet Muhammad (peace be upon him)
Islam
The leader of Islam after prophet Muhammad (peace be upon him) is Abou Bakr Assedique (may God be pleased with him).
The first Islam leader is prophet Muhammad (Peace be upon him) who conveyed God message to humanity and called people to Islam and conveyed to people the words of Quran as revealed to him by God. After prophet Muhammad death, Muslim leaders are called Caliphs, Imams, Sultans, Princes of believers. ...
As far as I am aware Islam does not have a single spiritual leader, in the same way that Christianity has the Pope. Until the end of the Ottoman Empire (1918) the sultan of the Ottoman Empire was the de facto spiritual leader of Islam.