Informally say "I'm sorry" vs. formally apologize

1. When you accidentally bump into a colleague of the opposite sex in the hallway, resulting in incidental body contact, you say "I'm sorry"; if the person you carelessly bump into, on the other hand, is your boss of the opposite sex, you apologize.

2. When your once-in-a-while slip of the bad-hair-day variety results in slight personal embarrassment when your boss inquires about it, you say "I'm sorry"; if the slip is so glaring, on the other hand, as to embarrass your boss in front of his/her boss, you apologize.

3. For whatever reason, whenever you sense that you owe something to your serious partner of crime at work (e.g., a team/project-mate who has gone through thick and thin with you over the years), you apologize; if, on the other hand, the person who thinks that he/she is owed something is a hapless bum who cannot put two and two together but blames everybody else but him/herself for anything that goes wrong, you say "I'm sorry, pal, but that is something you yourself would have to deal with."