First and Second Party Developers

[Kantor]

What, exactly, is the difference?

I know that a first party is owned entirely by one of the console manufacturers, and second party is partly owned or contractually tied to the developer. But what does this mean in terms of freedom? Can a second party developer split from a manufacturer, like Bungie? Was Bungie first or second party?

And what is it when, like Mass Effect, Microsoft takes a third party company and publishes the game? two and a halfth party? Or was Bioware second party as well?

Please help me clear this up.