Gillette section of the ShaveWiki, which has links to encylopedic entries for most varieties.
Also, if you haven't yet found your way to Achim's Mr. Razor site, you're missing out on a wonderful photographic reference!
In brief, the New Improved was the next Gillette evolution after the Old Type, changing the head configuration to provide more blade bend and gap (and adding a big dose of razor beauty as well). Next came the NEW, which had significant changes in head geometry, and they ditched the posts on the cap and the corresponding holes in the guard plate, going instead with a tongue-in-groove fitment (requiring new blades as well, since the 3-hole variety wouldn't fit anymore). The NEW De Luxe was essentially a "missing link" between the two; a New Improved head geometry with the tongue-in-groove fitment (and a slightly heavier head as a result).