The whitebook is just a plain black-and white book, and will be of more book-sized dimensions. It is specifically formatted for readability and usability at the table, for those who want "just the rules." There will be art, but it will be lower-rez, and not in color.
The Deluxe edition will be the actual book that this project is ultimately funding, to be released after final assembly and printing. It will be full-color, 6x9 glossy, with dual autographs, personalized tip-ins, and more features to be added as the project hits stretch goals.
The Limited version is a one-time graphic novel sized print in glossy hardcover. The entire book will be specially laid-out and rearranged just for this singular printing, and will include a special hard slip-case. Should there be funded the art book and graphic novel, they will all three be included in the slip case.
There are stretch goals on the page which could change/improve the current intended design, as well.
UPDATE 11/6/2012: This question was asked again in a recent G+ post of mine, so I felt I should copy-paste the answer I gave there to help pad this one out:
The whitebook will be a more or less "cheap" print. It's intended to be a rules reference and little more. It will have the same dimensions as the final book, just black and white, basic quality. Depending on how much extra it costs, and how many get ordered, I'm actually considering having them spiral-bound, just to make them easier to use at the table.
The "deluxe" edition is the intended released book, with some signatures, tip ins, and such. It's my end goal. The more money I make, the cooler this book will be. Very little of this KS is going to the printing costs, as I've got that covered with my personal cash set aside. Most of the cost is going into adding art to this Deluxe book.
The extreme limited edition is a one-time print. There will likely be some left over after the print is done and the backer rewards mailed out, which I'll sell for marked-up price online, or use as prizes at special gaming events or such. This is the ultimate version, with everything in the Deluxe plus everything that gets unlocked as stretch goals. The quality will be as awesome as I can humanly make it, in a larger graphic novel format.