There is no branch for it and there is also no "leader of THE religion". The leader, however, does not only need to be a respected person, but needs to be knowledgeable in the Quran (The Holy Book of Islam) and the Sunnah (The way of the Prophet Muhammad SAW) (What the Prophet did and what he said). Leaders could be of the Prophet Muhammad SAW's blood, but not every single one is.
For example, after the Prophet's death, his closest companion, Abu Bakr, became the leader because he was knowledgeable, was very just, and was the best Muslim during that time period. After 3 other leaders in Medina, then was a relative of the Prophet, but after him, his sons did not become leaders.
After this though, that's when another group of "Muslims" came who thought that Ali, who was the 4th leader and related to the prophet, should have been the first leader after the Prophet and then his descendants.
However, this is wrong.
So, all in all, there is no branch for what you're asking. There are only the Five Pillars of Islam and the Six pillars of Iman (Faith).
The 5 Pillars are:
1. Shahadah (Declaration of believing in the oneness of Allah (God) and that Prophet Muhammad is the last Prophet)
2. Salah (Prayer)
3. Zakat (Charity)
4. Saum (Fasting)
5. Hajj
The 6 Pillars of Iman (Faith) are:
1. Belief in Allah
2. Belief in the Angels
3. Belief in the Books
4. Belief in the Prophets
5. Belief in the Last Day
6. Belief in Al-Qadar (Divine Decree) (Destiny)