Radical Muslim, Moderate Muslim

Well put.

There is also another way to distinguish between Muslims of various degrees of militancy. Rather than the self-contradictory expression "moderate Muslims", invented by the West for tactical (read "cowardly") reasons and not used by the Islamic world, I prefer to call "devout and observant Muslims" the Mohammedans who are usually referred to as "radical and extremist", with the implication that those of them who are not covered by this description are not Muslim in the truest sense.