Anions are atoms or radicals (groups of atoms), that have gained electrons. Since they now have more electrons than protons, anions have a negative charge. For example, chloride ions Cl- , bromide Br- , iodide I-. These are monovalent anions, meaning they have a valency (combining capacity) with only one ion of hydrogen. Similarly there are bivalent anions, etc.
An ion is an atom (or group of atoms) with an electrical charge. Anions are one of the two types of ions. The other type is called a Cation, having a positive charge. In many crystals the anions are bigger; the little cations fit into the spaces between them.