Head over to the dining board and it explains most of these in more detail, but to answer your question in a nutshell..
ADR: Advanced Dining Resevations. Disney table service TS) restaurants take reservations. You will need to make one if you plan on dining at a TS place.
Dining Experience is a discount program for Florida residents only I think.
Free Dining is the
Disney Dining plan that you can book with your vacation package which is usually about $40 a day per person. You get a certain amount of dining credits each night you stay to use at Disney restaurants. In the early fall, Disney has offered the dining plan for free hence "free Dining".
Allears.net also has a lot of info on all of these and everything Disney...
