Now I'm wondering, do we have these terms defined effectively?
Radical, according to every dictionary I've read, is about change, not about moral content. A radical pushes for extensive and fundamental change.
Militant is advocating violence and force for your agenda, which isn't necessarily radical. A militant conservative might want to see people jailed for advocating change. If he wanted to see the articles of confederation restored and was willing to kill to do it, then he'd be a radical himself.
Extremism is the one I have an issue with. Like radicalism, people seem to mostly put extremism on a moral hinge and it becomes a thought-terminating cliche. If I'm a Christian, and I see the part of the Bible that says homosexuality is an abomination and gays /must/ be put to death, what's "extreme" about acting consistently with the principles of my worldview? It's "bad," it's "immoral," I should "go to jail" if I do it, but "extreme?" I dunno, man. A priori it's pretty reasonable. When someone makes an internally logical conclusion that you don't like, you call it extreme. People who advocate banning guns don't see banning guns as extreme, they see it as the obvious logical response. People who don't want to ban guns say it's extreme, you should do something not as significant.
If I had to define "extremism" I'd say "consistency you don't like."
And along those lines, I've seen the videos and news people posted in response to the thing I said about the moderate Muslims I know. Yeah. I think religion is a key factor here, one religion in particular but I'm certainly not a fan of most of the others. They are all-encompassing worldviews with dangerous contents.
This is turning into an essay, but one last word I don't like: "radicalization." To me at least "radicalization," aside from the stuff I said above about "radical" puts the blame at least partly on us. Arguments about radicalization often implicitly or explicitly say that western treatment of Muslims is what drives these behaviors. "ISIS wants us to respond with force because that'll increase recruitment."
Buddy, if you're telling me that the average friendly Muslim dude down the street is one microaggression away from becoming a suicide bomber, maybe you're not on the side you think you're arguing for.