To elaborate on Dan's answer:
Letterboxing merely uses the visible horizontal lines you see, and the black bars are part of the total image, and are recorded, taking up 'space'. The lines used to display the black are wasted lines.
Anamorphic widescreen uses all of the available horizontal lines, and then squeezes the image sideways so the entire frame is used, but not proportioned right for display.
When displayed, the picture is "unsqueezed" sideways, but then reduced in size proportionally, so the sides of the image fit the screen, so it looks like letterboxing, but with a difference:
The difference is that all of the lines are squeezed vertically when the image is reduced, and the black bars are filled in electronically. Therefore, all 525 (theoretical) horizontal lines are used in the letterbox-sized image.
So, the difference between letterboxing and anamorphic is the quantity of horizontal lines that are fit into the same-sized image, which means that anamorphic has a higher resolution, i.e., a sharper image.
Actually, any display device that can be adjusted for vertical size can be used to display anamorphic widescreen. TV's are normally not adjustable, which is why the capability must be built into the device, and be defeatable for non-anamorphic video.
Make sense?
Larry
www.fineelectricco.com