Different Actions. Anticoagulants are medicines which keep the blood from clotting by action on factors in the blood which are needed to stop bleeding. Oral examples would include warfarin and a new agent pradaxa. Anti-platelet medications interfer with platelet function making them less "sticky" hence less likely to cause a thrombus. Oral examples would include aspirin, plavix, (clopidogrel) and effient.
Good question. Clotting involves a chain-reaction of biologically active proteins in the body. This "coagulation cascade" culminates in formation of fibrin, a substance that is the bulk of clots. However, clots are also comprised of platelets, a type of blood cell that adheres to the fibrin. Anticoagulants specifically inhibit steps in the chain-reaction of proteins, whereas anti-platelets inhibit these cells.