After the death of Prophet Mohammed, people who believed his successor is his son-in-law Hazrat Ali who will guide the umma in spiritual matters as well as daily matters, hand-in-hand with Holy book Quran are called as Shia. While people who believed that after the death, Quran (the holy book) and Sunna (prophet' deeds) are sufficient for guidance in all spiritual as well as daily matters are called Sunni's.
Shia people believe in living Imam (Ali was first Imam) who is responsible for interpretation of the verse in Quran as per change in world.
Sunni people interpret the Quran themselves or look for educated theologies experts for guidance.
