Nintendo DS and DS Lite are exactly the same except with a few different features on the actual console. A DS game will work on Nintendo DS, DS Lite and DSi as they are all the same platform.
Yes. A DS Lite is the same as the DS, but smaller; A DSi is the same thing as a DS Lite but with a few added features. All DS games are compatible with all the kinds of DS, except ones that need the...
Not really, 'Nintendo DS' can mean any version of the DS, but specifically would mean the 'phat' DS which is the first, original version. (it's bigger than the DS Lite)