The full equations show the actual species involved in the reaction and the spectator (balancing) ions.
The balancing ions really do not matter. However, if you wish to generate a "full" equation, you only have to add the ions that go with the reacting species.
For example, in the reaction between iodine and sodium thiosulfate:
2S2O32- + I2 ==> S4O62- + 2I-
The ionic equation shows only the reacting species and ignores the sodium ions. But if you wish to include sodium, then for every thiosulfate you need two sodium ions:
2Na2S2O3 + I2 ==> Na2S4O6 + 2NaI
Don't forget that ionic compounds in solution are dissociated 100%, so the sodium ions are just floating around in the solution both before and after the redox reaction. They are mere spectators to the reaction.