Well, an alpine binding is obviously fixed at both points allowing no boot movement excepting for normal forward (and rear if you have a pair of sissy boots with a walk setting [img]tongue.gif[/img] ) flex. Heel and toe are locked down , and the boot is stiff in both directions with little flex forward and none sideways.
Telemark (also known as free-heeling) is binding that uses a soft boot with unlimited fore-aft flex, but with excellent side to side flex. these clamp in at the toe, and incorporate a strap (usually) that goes around the back which holds the boot in to the to piece but doesn't actually hinder you from picking your heel up from the binding. This is a completely differnt animal than alpine skiing requiring complelely different skis, techniques and boots. It is reminiscant of old school cross country skiing in that the foot flexes forward and the heel lifts up in every turn like you would when you are normally walking.
Randonee binding is asimiliar concept to alpine bindings and generally uses the same technique and control as alpine skiing, but with good backcountry maneuvarability as in telemark. You can unlock the heel piece fom the ski to make climbing easier, but lock the heel back down when you are ready to descend. These use a softer than normal randonee boot which is designed to be more comfortable for sweating up a hill than for performance while ripping down it. The boot is allowed to actually flex forward when skinning up a hill (alluding to the practice of putting an animal skin on the ski base when climbing up hill to keep the ski from sliding back down after every step) which allows greater comfort than hiking in alpine boots.
Lastly are AT bindings which are similiar in concept to Randonee except that you use normal alpine boots and the entire binding is on a plate which pivots upwards with each step from a hinge at the toe. It allows the use of superior performing, yet less comfortable alpine boots. The binding is stiff and will not allow the boot to flex to give greater comfort, and when you reach the top of the hill, you lock the heal don, (as in randonee) and ski down alpine style
Hope this helps. If I am inaccurate in some aspect, someone please correct me.