Radical Islamism is a Western concept, but refers to both violent and political activities to replace democratic government with theocratic government ruling by sharia. It does not equate to terrorism, but is an effort to build long-term structures. The term appeared in the 9-11 Commission Report: "radical ideological movement (commonly known as Islamism or radical Islam) in the Islamic world ... which has spawned terrorist groups and violence across the globe."
Fighting radical Islamism does not equate to fighting a religion, although radicals often attempt to paint Western efforts in those terms, and Islamophobic rhetoric may give that impression. Anti-religious rhetoric, indeed, hurts the broad area of information operations as a part of grand strategy against actual threats.
The fight against specific factions, however, may involve theology or Islamic law. For example, a fatwa has traditionally been issued by recognized legal scholars, which the leaders of al-Qaeda are not. It has been proposed to attack the religious legitimacy of their rulings. 
Individual groups vary in their targeting, theology, nationalism, etc.
Priorities in armed jihad
One important distinction probably was originated by al-Qaeda, probably by Ayman al-Zawahiri, that of the near enemy and far enemy. The near enemy is characterized by Muslim governments that are considered, by their critics, to be insufficiently observant of Islamic law.
Sects as proxies
Within Shi'a, there can be conflict between the ultimate political authority being nonclerical, or, with the Iranian revolutionary movement, the wilayat al-faqih doctrine of "authority of the jurisprudent."
State and quasi-state support
- Mehdi Mozaffari (17 November 2003), "Is It Possible to Combat Radical Islamism Without Combating Islam?", History News Network, George Mason University
- Brian Drinkwine (January 26, 2009), "The Serpent in Our Garden: Al-Qa'ida and the Long War", Carlisle Papers, Strategic Studies Institute, U.S. Army War College