There is a subtle difference between saying "I'm sorry" and "I apologize". An apology is a formal admission of a wrongdoing. It may or may not be heartfelt — i.e., a person may apologize without feeling remorseful. On the other hand, saying "I am sorry" is usually seen as being a truer admission of regret. It is what is called a "heartfelt apology." If someone says he is sorry but does not feel any remorse, then he is said to be lying.
"I'm sorry" is also used to express sympathy. For example, "I'm sorry for your loss" can communicate sympathy following the death of a loved one. There is no such usage for "I apologize." An apology is only for wrongdoing.
edit Using "I Apologize" vs. "I'm Sorry"
- "When Karen's boyfriend cheated on her, she got angry and smashed the windshield of his car. She later apologized." In this example, Karen does not really regret her action because she feels it was justified.
- Politicians often apologize for their gaffes, but they seldom say they are sorry for their actions because saying so makes them appear weak. For example, Joe Barton famously apologized to BP for what he called a $20 billion "government shakedown" of the company. After facing harsh criticism for his remarks, he apologized, saying that they had been misconstrued. Jo Bonner of Alabama's 1st congressional district called Barton's apology "half-hearted" and believed Barton was more interested in saving his job than making things right.
- Another obvious scenario where there is a difference is when one is expressing sympathy. One might say, "I am sorry your children fell sick before the camping trip," but it would be absurd to say "I apologize" in this case because the one speaking is not responsible for the children's illness.
edit Quotes About Apologizing
- It is a good rule in life never to apologize. The right sort of people do not want apologies, and the wrong sort take a mean advantage of them. —P.G. Wodehouse
- A stiff apology is a second insult.... The injured party does not want to be compensated because he has been wronged; he wants to be healed because he has been hurt. —G.K. Chesterton
- True remorse is never just a regret over consequence; it is a regret over motive. —Mignon McLaughlin, The Neurotic's Notebook, 1960