It's basicly the gameboy generation all over again (http://www.vgchartz.com/forum/thread.php?id=65421).
Appart from the ovbious paralelism between DS=GB and DSi=GBC if you take software into consideration. There is also another one, Firmware. The jump from DS to DSi is similar to that one that Nintendo did from Gamecube to Wii.
So yes, DSi is a different from DS, but totally backwards compatible.







