Firefox Developer Edition is built from the branch as Firefox Beta with some different settings. AFAIK it just has a different theme and extra debug assertions enabled.
It also lets you run extensions that are not from the Mozilla Addons site, there is no option for that in the standard edition.
That would be one of the different settings. For running unlisted extensions, iirc it's actually pretty trivial to get one signed; back when they abandoned Shumway it didn't take me more than a few minutes with the command line to get a signed xpi that I then installed on several computers. I might be remembering wrong, though.