There is a such a thing as a DSi game. They made games that could not be played on the DS. There is no such thing as a DS Lite game. A DS Lite game and a DS game are the same thing. That's the difference. A new platform is indicated by new software that only works on it. Prior to the 3DS coming out, DSi games were only playable on a DSi. So it's another system, just a REALLY lame one that had little to distinguish it. The GBC in comparison had some essential classics made for it.
Though I don't think the name "3DS" was ever meant to mean anything other than to emphasize its 3D capabilities.