One of the temptations when looking at any large organisation is the idea that it is monolithic. This leads to stereotypes and misconceptions, which is a disservice to everyone involved. Islam, like any great faith or organisation, is not a monolithic hive mind.
It is unfortunately divided into schools of thought, each with its differing interpretations of Islam’s holy texts and tenets. While the five pillars of the faith are consistent, details beyond those may vary based on what school of thought a Muslim belongs to.
The primary split between Sunni, Shiite, and Kharijite was initially political. However, the schism has become theological and juridical over time.
Sunni Islam is the largest of the three. Originally, they formed because they supported Abu Bakr Siddique to be the prophet Muhammad’s heir via election. They recognise the rule of the first four caliphs as legitimate. They believe that the caliphate may be chosen democratically.
Sunni Islam is divided into five sub-sects, with their differences on various matters.
Shia Islam, in turn, arose from the same dispute. Rather than support Abu Bakr, they believed that the Ahl al-Bayt (Muhammad’s immediate family and descendants) were the rightful heirs to the prophet. As such, these people have unique political and theological authority.
Shia divisions tend to be along the lines of jurisprudence, philosophical beliefs, and spirituality.
The two were, as pointed out, initially political divisions. Shiite theology only became a major focus of the divide after the secession of what would become the Kharijite sect.
There are few Kharijite sects in the world today. However, most Muslim groups use it to refer to any Muslim who refuses to compromise on anyone they disagree with. What few members of this sect remain espouse most of the original beliefs, but discard more aggressive tactics.
These major divisions themselves are not monolithic, with a variety of different schools under each. Schools of jurisprudence are the most common, but there are also varying spiritual practices and traditions. There are even theological divisions, dwelling on such topics as free will and predestination.
In short, Islam is a faith that has strong recurring commonalities. However, it is also one that has become divided over time due to natural human differences.