All three methods refer to cooking in liquid on top of the stove, but with different temperatures. Many dishes described as boiled are in fact poached or simmered. When water is heated up just enough to 'vibrate' at about 82 degrees C, it is perfect for poaching fish and other delicate foods that would otherwise break up.
A gentle simmer at 85-93 degrees C produces liquid that hardly moves except for occasional bubbles in the same place (ideal for cooking joints of meat and whole birds).
A true boil is used for the quick cooking of vegetables, rice and pasta, and some cereals. A gentle boil is used to reduce liquids when making jams and sauces.
** Asian Online Recipes