Objectivity is sticking to the facts, being guided by the evidence and considering an event will be closer to the truth the more supporting evidence it has. This is important when gathering evidences during the audit.
Meanwhile, impartiality is not taking sides, to give up making value judgments and treat as equivalent different versions of an event, believing the truth is in the middle. This is important when making decisions based on the evidence you've acquired during the audit. For example, if you are conducting the audit and making the report or conclusions based on evidence in a way that purposely benefits or mitigates responsibility of certain people for certain audit findings (e.g. nonconformities).