Shia and Sunni are the two main branches of Islam. The major difference between them is their belief on who should have succeeded Prophet Muhammad after his death.
Shia Muslims believe that Ali, the cousin and son-in-law of Prophet Muhammad, should have succeeded him. They also believe in the concept of imamate, which is the belief that the Imam, a divinely appointed leader, has a special spiritual connection with God and is required for the spiritual and political guidance of the community.
Sunni Muslims, on the other hand, believe that the first four caliphs, who were elected by the community after the death of Prophet Muhammad, were rightful successors. They do not believe in the concept of imamate as it is believed in Shia Islam.
There is no inherent difference between the two branches in terms of their level of fundamentalism or terrorist views. Both have moderate and extremist factions within them. Extremist groups such as al-Qaeda and ISIS are predominantly Sunni, but it is important to note that the vast majority of Sunni Muslims condemns their actions. Shia Muslims have also been targeted by terrorism, with extremist groups such as the Taliban targeting Shia mosques and shrines.
Overall, it is important to recognize that the vast majority of both Sunni and Shia Muslims are peaceful and do not support extremist or terrorist views.