The circumstances of the apology are also important, and should be carefully planned.
Many people appreciate a written apology, because it implies time and effort put into this step toward reconciliation.
Some people who have been offended want an opportunity to state the intensity of their pain or embarrassment directly to the offender.
Some people would appreciate a face-to-face apology, and a chance to shake hands or otherwise take the next step toward improved future relations.
Some people who apologize want an acknowledgement that the apology has been received, or that the offender is forgiven.