Hi Rymer,
The walking foot is for doing straight quilting using the feed dogs. You would use this for SID, straight outline quilting, like a 1/4" echo from your seams or an all over straight grid. The walking foot acts like a regular presser foot but has an attaching lever (for lack of a better word, sometimes looks like a tuning fork) which attaches to the needle shank, the part of your sewing machine that holds the needle. This allows the foot to move up and down with your needle "walking" along the quilt sandwich ensuring even feed of top and bottom layers.
The darning foot also known as a big foot, open foot and I have even heard it referred to as an embroidery foot you use with the feed dogs disengaged or in the "down" position. The quilt sandwich is moved under the needle by you, the machine does no movement of the quilt sandwich because the feed dogs are down. This is the foot for FMQ which is things like the meander (aka stippling), circles, pebbling, feathers, or any free motion design where you want to quilt in any direction.
Check out Leah's free motion quilt blog for more info on FMQ. She did a great job putting this together and gives lots of inspiration and hints for FMQ. Her blog is
http://www.freemotionquilting.blogspot.com/