There are a number of different "widescreen" ratios; 16:9 and 2.35:1 are the two most common.
Letterbox and Anamorphic widescreen are two types of widescreen formats. Letterbox was developed for VHS; the original widescreen master has the black bars added to the top and bottom, so even though letterbox is widescreen, it is stored on the VHS/DVD at 4:3. In effect, the movie, not including the black bars, is stored on a DVD at 640x320.
Anamorphic widescreen was introduced with DVDs; it stores the movie on the disc at its widescreen ratio. Then, if your TV is 4:3, the DVD player will toss out every fourth line and add the black bars on the top and bottom before displaying the movie on the DVD. The advantage over Letterbox is that it is stored at an effective resolution of 720x480 (for 16:9). While Letterbox doesn't look much different than anamorphic on a normal 4:3 TVs (except for Wegas with their anamorphic squeeze option), letterbox will look like crap on 16:9 HDTVs because it will have to blow up the lower resolution picture to fill the screen.