Is this happening after every time you stop, or only when you first start the car and start rolling in the morning? The latter would be the pads actually sticking (via slight oxidation) to the rotors. You actually have to break them loose. I've had my pads changed to Motorcrafts with a lower metal content, and they no longer weld themselves to the rotors, and (knock on wood) I haven't warped my rotors since the change.
Now, not having any vehicle info or history here, it sounds like you have something rusty or pitted, e.g., caliper slide pins, that are preventing your pads and/or shoes from moving freely when you release the brake pedal. If things are bound up, releasing the brake pedal would result in everything "popping" back into place instead of sliding.
Not much substitute for getting the car on a lift and taking the wheels off. A brake inspection by a competent shop should do the trick.
Good luck!
