NEWS: Brad Warner's Hardcore Zen: Santa Claus Died for Your Sins

To quote your second source, "[Non-theism]'s use can be applied to the ideas of atheism (both weak and strong), agnosticism, ignosticism, and skepticism..."
Strong and weak atheism would basically be equivalent to my reference to militant vs typical atheists, though I do prefer the strong vs weak terminology to what I used.
....A rose by any other name? Though I do retract my statement that non-theism IS atheism... it can also be agnosticism, which in reality I did understand, but didn't state my point as such.

Also
"Originally coined as synonymous with secularism, [non-theism] has become an umbrella term for summarizing various distinct and even mutually exclusive positions united by a naturalist approach..."

So, thanks for the links, but I still maintain my previous position. I think people most often use this term either when they are confused about how they really feel on the topic of God/gods and all that jazz (which I have no problem with,) or when they aren't yet able to face the music and accept that they are, infact, atheist or agnostic or whatever the hell else they are (which I do have a problem with.) Saying that non-theists are different from atheists in that they don't think about God/religion is rubbish, for all the reasons Toku666 so eloquently stated.