If you'd have said that an ion is any atom or molecule that contains an unequal number of protons and electrons, you'd have been basically correct.
Ionization, however, can happen between almost any two atoms, molecules, or atoms and molecules. While a classical example of an ionic substance is a salt such as NaCl (where Na gives an electron to Cl), in organic compounds acid-base reactions are all about ionization (for example, when HCl dissociates into H+ and Cl-) or de-ionization (for lack of a better word) (the reaction between H+ and OH+ to produce water).