Final answer:
The denominations of Islam described are Sunni and Shia.
Step-by-step explanation:
The details described in the question refer to the denominations of Islam, specifically Sunni and Shia.
The Sunni denomination comprises the majority of Muslims worldwide, around 75-90%. They follow the customs and interpretation of the Quran based on the hadith, and accept Abu Bakr as the first leader after Muhammad's death.
The Shia denomination, making up around 10-20% of Muslims, believes in the leadership of Ali and his descendants. They are known as the followers of Ali.