What distinguishes the peaceful Muslim's faith with the notion of Islam followed by those who advocated a radicalized form of the religion?
I am fairly confident that there will be many different approaches to this question. It is not an easy one, and I would preface it by saying that the thoughts generated here might simply be a starting point for more discussion on the topic.
I think that one of the distinguishing points between a radicalized notion of Islam and other interpretations of the religion is its belief in inclusiveness and acceptance. I think that the version of Islam seen in its most radicalized and most fundamental form has strict interpretations and analyses that make it different than other versions. At the same time, though, this is no different than any other form of religion. Fundamentalist versions of all religions demonstrate themselves to be more stringent and less tolerant of embracing multiplicity and divergent approaches to spirituality. In this, fundamentalist versions of the religion are less willing to embrace different paths to spiritual identity. It is here, within this level of perceived stringency, that radical Islam appeals to those who so closely align themselves with aims of terrorism. Such an interpretation can be used to isolate and divide and enable those in the position of power to advocate or consolidate their own sense of power within the fundamentalist interpretation.