There is a difference between saying ‘I’m sorry’ and ‘I apologize’. An apology is an admission of an offence or failure. A person can give an apology without feeling remorseful. Usually, when people say ‘I’m sorry’, they have a stronger sense of regret for the incident. Furthermore, ‘I’m sorry’ can be used to express sympathy e.g. saying ‘I’m sorry for your loss’ at a funeral. However, ‘I apologize’ is only used for wrongdoing and does not have a function to express sympathy.