Sorry for the necro-lite... I know this topic hasn't been touched in about a month, but I wanted to give a little perspective on my perceived difference between the "Indie" and "Homebrew" scenes. Feel free to take with a grain of salt, as I tend to have a rather bizarre logic controller inside.
To put it simply, the homebrew scene is a primarily hacker-centric community. I'm not talking about black-hat hacking, but the kind of tinkering that is exhibited in the industrious and creative personalities. They do it for the thrill of creating something that is their own. That isn't to say that they don't "borrow" elements (anything from using other people's tiles, to almost entire products with mere tweaks), but they do like to have it their way. Their own spin to an old idea.
As for indies/independents, they tend to be more on the business-side, as has been previously suggested. Indies want to take their hobby a step further, and do it for a living, and/or fame and notoriety. They tend to "borrow" less, and want as much creative freedom/control over their product as possible. They also tend to target more mainstream markets, as there is usually a fiscal motive behind things (not to say indie devs are all about money; just that it is usually a consideration -- more so than for homebrewers).
I've been primarily an indie developer for the past decade+, but my focus has tended to go more toward what I perceive as the homebrew line. Making an NES game has been a dream of mine since I first got an NES. Things like the Atari et al didn't inspire me in that way. So, I decided to stop trying to "change the world" as an indie developer, and focus on what I want as a homebrewer.
Of course, there are various interweaving characteristics between indies and homebrewers, so the differences are relatively fuzzy... but the descriptions I gave are what I've observed from hanging around the gaming scene for about the past 30 years.
![Smile :)](./images/smilies/icon_smile.gif)