Islamic extremism refers to two related and partially overlapping but also distinct aspects of extremist interpretations and pursuits of Islamic ideology:
an extremely conservative view of Islam, which doesn't necessarily entail violence even though it may have an emphasis on Jihad; see Islamic fundamentalism, and
the use of extreme tactics such as bombing and assassinations for achieving perceived Islamic goals; see Jihadism.
In Islam word for Islamic Extremist is Khawarij. From their essentially political position, the Kharijites developed extreme doctrines that further set them apart from both mainstream Sunni and Shiʿa Muslims. The Kharijites were particularly noted for adopting a radical approach to Takfir, whereby they declared other Muslims to be unbelievers and therefore deemed them worthy of death. The Kharijites were also known historically as the Shurah (Arabic: الشُراة, translit.: Shurāh),[A] literally meaning "the buyers" and understood within the context of Islamic scripture and philosophy to mean "those who have traded the mortal life (al-Dunya) for the other life [with God] (al-Aakhirah)", which, unlike the term Kharijite, was one that many Kharijites used to describe themselves.
Zeyno Baran, Senior Fellow and Director of the Center for Eurasian Policy at the Hudson Institute, argues Islamist extremism and Islamism are better terms, to distinguish the political ideology from the religion.