What is a Muslim extremist?

Six Muslim men are at the moment standing trial for attempting to explode a bomb at an EDL rally.
The Daily Express refers to them as "Muslim extremists.  I would like to know what a Muslim extremist actually is.

First, what is an extremist?  Presumably it is someone who adopts an extreme point of view, someone who is not a moderate. But who is to decide what constitutes an extreme point of view?  Or indeed a moderate point of view?  Are these things not in the eye of the beholder?

I try to avoid using the words extremist and extremism because I recognise that they are meaningless.

Second, even if we allow that the concept of extremism exists, what is a Muslim extremist?

I have already in previous posts cited passages of The Koran which incite violence and even murder. Therefore, a Muslim who attempts to murder non-Muslims can reasonably be described merely as a Muslim.  Qualifications like extremist and fanatic are redundant.