Seems... Heartless are creatures without hearts or more accurately, the raw darkness dwelling within any heart taking on a form of its own. Heartless have always existed because darkness has always existed just as has light. Because of Xehanort's strong heart, he was able to maintain his physical form (this is notable of all the Disney villains as well). Kairi never became a Heartless because her heart migrated to Sora's body instead. Sora then regained his form after Kairi shared her light with him. Riku willingly delved into the darkness but as he was possessed by Xehanort's Heartless, he never actually became a Heartless himself. This makes these four characters unique.
Nobodies are bodies left behind. They are called Nobodies because they have no real identity. They are nothing. Without their hearts, they can't experience or express emotion (apparently rage and despair are not true emotions, possibly derivative of the fact they are products of darkness). Nobodies can only be formed from people whose desires surpassed the strength of their hearts... as I put it. This leaves leftover desire in the body once the heart has left.
The Unbirths are obviously meant to embody characters that were never born. To be born, you must come into existence with a body, a heart, and most importantly, a soul. Obviously, Unbirths must be without souls. This would make them but a representation of the body and heart. Emotional, infantile, random, indecisive... not clear whose side they're on, probably. I wouldn't be surprised if some of the Unbirths don't fight you.
