They are very different things.
The
Disney Dining Plan is a pre-paid dining plan where for a fixed price per day (#38.99 adult right now I think), you get one Table Service, one Counter Service, and one Snack (less than $4) per day. You HAVE to get the plan for every night of your stay at a Disney Resort, and you can only get it if you are staying at a Disney Resort. There is a whole subforum on the topic.
The Disney Dining Experience is $85 for Florida Residents or $65 for Annual Passholders . It is a discount card, good at most all Table Service restaurants for 20% off your bill. There are restrictions, such as it isn't valid on major holidays, etc. Allears.net has a good list of where it is good. I think there are a few CS places you can use it at resorts that don't have a TS restaurant. The DDE card is good for a year from the time you order it, and depending when in the month you order it, 13 months (I'm not sure of the cutoff date). You must have an Annual Pass or at least the voucher to get it. Not sure what a FL resident must do...
Edit: forgot - it is a discount for the cardholder and up to 9 guests, and includes alcohol drinks. THe cardholder must be present.