What does it mean to be a "radicalized" Muslim?

Tom Krannawitter asks a good question today:

For those who perhaps have spent more time studying the Qur'an than have I, please offer some enlightenment:

I am having a difficult time understanding what is meant by the phrase popular among news media talking heads and some politicos of Muslims being "radicalized." What exactly does "radicalized" mean in this context?

I have studied the Qur'an enough to know that Islam views legitimate religious authority and legitimate legal or government authority as essentially the same thing.

It takes a stretch of interpretative imagination to deduce something like "separation of church and state" from the Qur'an, which provides a detailed guide for the lives of Muslims individually, socially, and politically -- including detailed punishments for a host of Qur'anic "sins." For Muslims who believe that the Qur'an is literally the word and authority of the one and only God, how could they ever concede that, say, some man-made Constitution is more authoritative than the Qur'an in any situation?

I've also read over the Qur'anic passages providing injunctions for Muslims to engage in violence, including detailed instructions of how to cut off hands and feet, decapitate, and "strike off the fingertips" of "non-believers." The Qur'an makes clear that such violence should persist until "all religion is for Allah." (Surah 8:39)

So it seems to me that there are essentially two kinds of Muslims: There are Muslims, who piously obey the Qur'an including its commands to engage in violence and kill and torture non-believers. And there are apostate Muslims, meaning Muslims who have for the most part abandoned Islam in belief, in practice, or both. This is what religious "apostasy" means.

If I am correct -- and, again, I ask kindly to be righted if I am wrong -- then what might it mean for a Muslim to be "radicalized?" How does a "radical Muslim" differ from a "Muslim?" Is being "radicalized" just another way of saying a Muslim who did not take his faith or the teachings of the Qur'an seriously before, now, all of sudden, IS taking his faith and the Qur'an seriously? Or does it mean something else?