Let me begin by saying that I am by no means an expert, but rather an enthusiat who tries to stay well informed. I make every effort to not pass on false information, but if somebody notices something here that is incorrect, I would welcome the criticism and hope that you show me the error in my ways.
Here's the deal. Pan & Scan (also called Fullscreen) is a process done either in the film to video transfer stage, or from the video masters to convert a wide image (1.85:1, 2.35:1, etc..) to one that will fit on the vast majority of television screens, which are 4:3. An editor (sometimes with the help of the director) will position a 4:3 frame over the OAR (original aspect ratio) image. Sometimes the P&S frame will be in the middle of the OAR image, sometimes off to the side, and very often will move from left to right (or right to left) during a shot. This is not the same as your Zoom feature on either your DVD player or TV; that just enlarges the image and always shows the middle portion. Pan & Scan is a process that cannot be easily approximated by a player, and thus requires it's own, seperate track on a DVD. Setting your DVD player to send a 16:9 signal should have no effect, because the entire signal has an aspect ratio of 4:3.
Letterboxed images are also designed specifically for a 4:3 TV. The OAR image is encoded with black bars above and below the image; the black bars are part of a complete image with a 4:3 aspect ratio that is encoded on a disc. When shown on a widescreen TV (16:9 or, 1.78:1) the black bars above and below the film image will be visible, and there will also be space on either side of the image that must be filled in by the TV. It is a 4:3 image (with black bars at top and bottom) set in the middle of a 16:9 frame. When viewed with a regular 4:3 TV a letterboxed image will fill the screen side to side and have black bars top and bottom. (Note: the size of the black bars in both letterbox and anamorphic tranfers are dependant on the OAR of the film. A 2.35:1 movie will have larger bars than a 1.85:1 movie, or said in a different way, on the same TV a 2.35:1 image will be shorter than a 1.85:1 image.) Like Pan & Scan, or Fullscreen , setting your DVD player to output a 16:9 signal will have no effect, as there is no 16:9 signal present (letterbox is 4:3, remember?)
Anamorphic DVD's present a different challenge, though. Essentially these discs are optimized for people with projectors and widescreen TV's. The OAR image (let's pretend it's 1.85:1) is compressed side to side during the encoding process. When this now 16:9 bitstream is fed to a 4:3 TV the image looks tall and squeezed. This is because the 4:3 TV cannot apply the horizontal resolution properly (it's a 16:9 image, right?) but it can realize the full vertical resolution - so the image looks like it's squeezed from left to right and rather than being 1.85:1 it looks closer to 1.33:1, and thus, tall. When this bitstream is fed to a 16:9 TV (or projector) the horizontal resolution can be spread out over the full width of the screen - since you can now realize both the full horizontal and vertical resolution the OAR has been restored. A standard 4:3 TV can still be used for anamorphic discs, though. The DVD player must be set for 4:3, and then the player will downconvert the anamorphic image, essentially discarding some of the lines, in order to shorten the picture (top to bottom) and restore the OAR. Not all DVD players do this equally well, though. Most are pretty good.
Anamorphic discs are "future proof" in the sense that many people's next TV will be 16:9. Letterboxed discs, although they seem to produce the same picture as an anamorphic disc on a 4:3 set, are vastly inferior when viewed on a 16:9 set. As an aside you should note the aspect ratio of these 16:9 TV's is really 1.78:1, and few discs are actually produced with that ratio. Most discs tend to be 1.85:1 or 2.35:1, and both of these, even when viewed on a widescreen set, will produce some level of black bars.
As far as how the information is stored on the DVD, I'm pretty sure that it's stored as 480i. Progressive players can recreate the 480p picture internally, or your TV can do with a line doubler/scaler. There are a few ways, but the best is for the player to do it BEFORE converting the signal to analog. The best players can detect "flags" imbedded in the bitstream and use those to help them piece back together the 480p image, essentially reversing the 3-2 pulldown process that's used to go from film to video in the first place. I'm no expert though. If the process interests you, let me know and I'll see if I can dig up some links. Enjoy.