I voted homebrew hybrid, but I'm not sure that's accurate.
For D&D, I feel no shame stealing classes, monsters, and other (IMO) heavily mechanical elements from published settings. I can either reflavor or work them into them world as is. The adventures/stories themselves, as well as the surrounding geography, are all mine. I've always found the published stuff to be lacking in those areas. So, the world is mine, but its populated with other people's stuff, usually.
Of course, I'm this way for D&D. For Fate, everything is homebrew because its just soo much easier than D&D. Other games I've played or run generally either "live" in modified real world or in a specific setting like Star Wars or Marvel.