DDE is Disney Dining and Entertainment card. You must be a FL resident or have an AP to purchase one for 60$ (pus 25 for a 2nd card). It entitles you to 20% discount on all food and beverages at most of the TS restaurants and a few of the CS ones, and half price admission to PI- and a few other perks such as free valet parking when dining.
DDP is the Disney Dining Plan, which is discussed at (much!) length here. It's a set fee per day to get 1 TS, 1 CS and one Snack per day per person- and you must be staying on property and buying at least a 1-day ticket, plus forgoing most room discounts. Many of us spend a lot of time weighing the options to see which works better in our situation- me, I go with the DDE unless dining is free!