You've heard the terms "radicalized Muslims" and "fundamentalist Muslims." We use those terms to make sure everyone knows we're not talking about "normal" or "moderate" Muslims. There is a good reason to try to make this distinction.
The main reason is because if you say "Muslim," you might mean all Muslims, and clearly all Muslims are not behaving the same.
The only piece of information missing from most peoples' understanding is that the "radicalized" Muslims are not really radical. They are orthodox. They are simply doing what it says in their scriptures they are supposed to do. They're not "hijacking" their religion or misinterpreting it. Most non-Muslims are unaware of this.
The first definition for "orthodox" in Answers.com is: Adhering to the accepted or traditional and established faith, especially in religion. That's perfect. And it is easily understood by most Westerners. It's a term we're already familiar with.
And in Answers.com, heterodox means: Not in agreement with accepted beliefs, especially in church doctrine or dogma. You can delete the word "church" and that's a great definition for what has been termed "moderate" Muslims. It's accurate and makes the distinction very clear.
So I'll be using the term "orthodox" to describe someone who strictly follows the teachings in the Quran and the Hadith, and who tries — as a good Muslim is supposed to do according to the doctrines — to follow Mohammad's example.
To learn more about some of these basic teachings and what kind of example Mohammad set, refer to the article, What Makes Islam So Successful?