varied diet definition versus balances
A moderate diet is like a balanced diet. Not extreme in any way: not extremely low fat, not extremely low carb, not extremely high sugar; everything is very moderate. However 'moderate' tends to be a VERY subjective term, because what is moderate for one person may not be moderate for another. A varied diet simply means you are not eating the same foods every day; the foods that you eat vary, which prevents you from becoming deficient in any nutrient.
It may not necessarily be optimal or have any variety. A balanced diet refers to a diet that does not have too much of just one thing. For instance, if you eat nothing but rice, pasta, potatoes, bread, and corn, then that is NOT a balanced diet because it has too many starches and not enough protein, fiber, or fat.