It's the same difference between Kleenex and facial tissue. One is a trademarked name for something, the other is the basic description of what it is. The problem with it (indoor football) being reported as Arena Football, is mostly the media's fault. True, there are a few teams that either let it happen, or did it deliberately, but for the most part, the media call it Arena Football, because that's the term they know and may not be aware that it's taboo to use.
I know for instance, the TV commercial for the Steubenville Stampede mentioned Arena Football. Since WTOV ran it, I'm not sure if they called it that to tie into the fact they aired the AFL, whether the guy doing the spot simply took a liberty of calling it that, or whether that's what the team told them to do.