There are so many ways of saying sorry or apologizing for your shortcomings and mistakes.
Excuse, forgive and pardon are three words we use for the same purpose but in different contexts depending on the intensity of the mistake made.

Excuse is used when the offence is trifling
Kindly excuse me for my carefree nature.

Forgive is used when the offence is slightly graver
Forgive him for the aggression he showed against his classmate.

Pardon is used when it is a serious offence
Pardon me for compromising my sanctity and integrity for this project.