Differentiate polyvalent ions from polyatomic ions.

Hint: The word poly- means many, so when a name has poly- as a prefix, we can assume that it will have many units of whatever is mentioned next.
Valency is the combining capacity of an element, meaning the ability of that element to combine with other elements, which is expressed in terms of numbers.

Complete step by step answer:
If we look at the terms given then the word itself gives the meaning because “poly “means more than one. So in polyvalent ions there is more than one valency and in polyatomic ions there is more than one atom.
So we can say that a polyatomic ion is a chemical species which has charge but it is having more than one atom. The ion can be positively charged or negatively charged. In case of polyatomic ion atoms are covalently bonded to each other. For example: Carbonate ion ($C{O_3}^{2 - }$) has one carbon atom and three oxygen atoms so it is a polyatomic ion.
On the other hand polyvalent ions are a chemical species which shows more than one valency. It means that an atom in an ion shows more than the valency of one. For example ${N^{3 - }}$ is a polyvalent ion in which nitrogen shows a valency of three. Similarly ${O^{2 - }},{S^{2 - }}$ are also polyvalent ions having the valency of two.
If we consider ammonium ion ( $N{H_4}^ + $) it is a polyatomic ion but it is not a polyvalent ion because the charge is one here.

Note:If we consider the theory behind the polyvalent and polyatomic ion polyvalent ion means it uses more than one electron in the formation of chemical bond on the other hand polyatomic ion uses more than one atom to form an ion. A polyatomic ion has two or more covalently bonded atoms that act as a single ion. The polyatomic ions form ionic bonds with other ions and form a single unit. There are so many polyatomic ions found in our body like bicarbonate ions, $HCO_3^ - $ which are important for various metabolic processes.