what are times that "I'm Sorry" and "I apologize" not the same thing?

@BiasForAction That Reminds me of something that happened in anger management group about a month ago. This new guy showed up, and I thought I'd be funny, which apparently has always a mistake. I said, "Greetings, new meat!" in kind of a creepy voice. He responded by telling me to call him sir. At least that's what I heard. Turns out his name was Ser. Like, who TF names their child Ser?

@LordShadowfire I have a pet dog named “Peeve”