Downloading Vs. Listenning to music online

So there's this war against downloading music and that whole hooplah. But I wonder if listenning to music online is, or should be considered, illegal as well.

Radio.Blog.Club. Here's a site where you can click onto most artists, and listen to the music. Now, how is this different from downloading? The consumer, or theif-whichever side of the coin you like-still gets to listen to the ENTIRE audio for free, and yet the artist gets no profit.

So how do they do it? Well, the creators are apparently taking cover under THIS. I've never seen this before.

They claim they're covered under a Creative Commons Deed. It says:

"You are free: to copy, distribute, display, and perform the work Under the following
conditions:
You must attribute the work in the manner specified by the author or licensor."

So what's the difference between putting it online and attributing it, and owning it and attributing it? How does that line get blurred? People can still listen to it for free, the artist doesn't get pain in either situation. So where do we draw the line?

Please correct me if I'm wrong, but according to that, I can legally make my own copy of someone's "work" so long as I attribute it?