"Whole hops" are just the cones. Some people call them "Whole Leaf" which is really a misnomer (named wrong). When used in a recipe it is common to use 10% more WH than pellet quantities unless the recipe specifies whole hops. Whole hop shelf life is shorter than pellets. All hops should be stored in a vacuum sealed bag in the freezer.
Pellets are pulverized whole hops. They are used per the recipe. Pellet shelf life is usually longer under the right conditions as they are formed tighter and have less of their surface exposed to the air.
Hop Cakes...that's a new one on me...let me know what kind of frosting you use...
Actually, I think you mean "plugs". These are whole hops that usually come in pre-weighed 1/2 oz form. See "whole hops".