There are two major differences between Sunnis and Shiites. One has to do with history and the other with scripture and religious authority.
Historically, these two Islamic sects differ as to who should have replaced Muhammad as leader of all Muslims. Shiites feel that Muhammad should have been succeeded by a blood relative. They wanted Ali, Muhammad’s cousin and son-in-law, to succeed him. The people who became the Sunnis followed Abu Bakr, who was appointed by an assembly to replace Muhammad.
In terms of scripture, Shiites believe that the Koran is the only source of religious authority. Sunnis, on the other hand, also believe that traditional accounts of the actions and sayings of Muhammad are authoritative. The Shiites do not believe that these accounts (many of which were written down by successors of Muhammad that the Shiites do not recognize as valid) should be accepted as sources of authority for how they should live their lives and how they should worship.