My question is – what is radical Islam and what is moderate Islam; surely there is just Islam?
		
		
	 
About 90% of Muslims are Sunni Muslims. That means by definition they strictly follow the Quran and the Sunnah of the Prophet Muhammad. The texts are available world wide and American Muslims practice Islam with the same rules and the same absoluteness as Muslims in every culture.
There is no 
organized group of Muslims who consciously do not fully follow Islam and still consider themselves practicing Muslims. Muslims who don't fully follow Islam are really not recognized by most Muslims in terms of giving them a separate label. They are simply people who are not that religious.
#1 People who do not fully follow Islam make that choice individually. 
#2 There is no 
group of people who have 
organized in order to not fully follow Islam. 
#3 There is no philosophy that exists that directs a person in which way to go about to not fully follow Islam. 
Therefore the term "Moderate Muslim" does not make sense because it does not describe any 
organized group of people. 
What is the definition of a "Moderate Muslim"? There is none. Muslims don't have one and non-Muslims don't have one.
The term "moderate Muslim" was not really used until after 9/11. It is a term that the media made popular in order to feed into the misconception that the 9/11 hijackers attacked America because they were practicing the true religion of Islam; that is to say, the implication is that "Moderate Muslims" are not fully practicing Islam and the true religion of Islam teaches violence. The media has obviously succeeded in deceiving most non-Muslims.
The vast majority of Muslims define Islam as a peaceful religion. Again the term "Moderate Muslim" is a concocted term but unfortunately some Muslims use it. However as I just explained the term does not have a definition and when some Muslims use it they do not necessarily believe it to mean what you take it to mean. But of course these Muslims have been tricked into spreading confusion about their own religion.
They know that  indiscriminate killing is not sanctioned by Islam so some Muslims label the Muslims that kill indiscriminately as "Radical". But the point they are attempting to make is that people who practice Islam fully and properly are "Moderate Muslims", i.e. 99% of Muslims are "Moderate Muslims" and therefore peaceful, and "Muslims" who kill indiscriminately are "Radical" Muslims. But Muslims who use the term "Moderate Muslims" are inadvertently, due to media propaganda, confusing people into thinking the exact opposite. When Muslims use the term "Moderate Muslim" they legitimize the term from the point of view of a non-Muslim. However the non-Muslim continues to define the term in the way that the media has portrayed it.
#1 Muslims use the term "Moderate Muslims" to refer to the true adherents of the teaching of Islam.
#2 The media has confused people into thinking that "Moderate Muslims" are people who do not truly adhere to the teachings of Islam.