“An apology, in the original sense of the word, was a pleading off from some charge or imputation, by explaining and defending one’s principles or conduct. It therefore amounted to a vindication. One who offers an apology, admits himself to have been, at least apparently, in the wrong, but brings forward some palliating circumstance, or tenders a frank acknowledgment, by way of reparation. We make an apology for some breach of propriety or decorum (like rude expressions, unbecoming conduct, etc.), or some deficiency in what might be reasonably expected. We offer an excuse when we have been guilty of some breach or neglect of duty; and we do it by way of extenuating our fault, and with a view to be forgiven. When an excuse has been accepted, an apology may still, in some cases, be necessary or appropriate. An excuse is not grounded on the claim of innocence, but is rather an appeal for favor resting on some collateral circumstance. An apology mostly respects the conduct of individuals toward each other as equals; it is a voluntary act produced by feelings of decorum, or a desire for the good opinion of others.”
— Crabb [Webster’s Dictionary, 1913]
Note: I couldn’t find out who this ‘Crabb’ person is! But the difference between an apology and an excuse was nicely explained. Hence I posted it.