what is the difference between a chlorite ion and a chlorate ion?

the different suffixes are used to indicate the oxidation state of the primary ion in the various possible oxyanions. Chlorine in chlorate has a more positive value compared to chlorine in chlorite. (same thing as sulfate versus sulfite). The oxyanion formed with those two chlorine atoms will either have a different net charge or a different number of attached oxygen atoms, or both.

The generic rules of formula writing says that we should provide the minimum ratio of elements, so SO4 would be used for sulfate (rather than S2O8), although there are exceptions when the structure is one that is not best described by following that rule (they usually are best described by that rule, so exceptions are uncommon although not existent=H2O2 would be an exception).

To know which ion is intended for the specific suffix, you need to know which charges to the main ion are possible and which are common. chlorate is the ion where Cl has a +5 charge, so the oxyanion is ClO3-. Chlorite is applied to the oxyanion containing Cl+3, or ClO2-

Cl can also be found in the +1 state (hypochlorite, such as sodium hypochlorite or bleach NaClO) and the +7 state (perchlorate, ClO4-). When Cl is present at -1, it is chloride-chloride is not an oxyanion.

There is nothing to do about this except learn the rules of nomenclature.

Chlorite ion is a doubly-charged multi-atomic anion which contains one chlorine atom and two oxygen atoms. Chlorate ion is also a doubly-charged multi-atomic anion which contains one chlorine atom and three oxygen atoms. The chemical formulae for chlorite and chlorate ions are ClO₂⁻ and ClO₃⁻ respectively.

A chlorite ion has one oxygen atom less than a chlorate ion.