That depends some on which part of chemistry you are in and which "-ates" and "ites" you are talking about.
In general chemistry and inorganic chemistry, things like sulfate, sulfite, nitrate, nitrite, chlorate, phosphate, are all complex anions containing multiple oxygen atoms bonded to an atom of another element (sulfur, nitrogen, chlorine, and phosporus for these examples). If the cation is a proton, you get acids - for example, sulfuric acid (H2SO4, could also be called hydrogen sulfate) - which are mostly liquids. With any other cation, you get salts - for example, sodium sulfate (Na2SO4) - which are mostly solids.
It will take you a while to get familiar with all the possibilities, but for now, "-ate" or "-ite" indicating a salt and a solid will be the right answer most of the time.