Say tomorrow I ruin a test at school. A reason would be: I was sick the two weeks before the test. An excuse: [I couldn't help it,] I was sick the day before!

I've done some stuff I needed to apologize for. I usually started with apologizing, then explained why I did it, then said I would try to do better in the future (but that I might not be able to). For example if I run out of class because I suddenly get scared of the teacher, I will email to apologize, because running out of class is never acceptable. I will then explain what happened, why I did it. Then I will state my intentions for the future.

An excuse would be more like "Sorry for running out of class, but I got scared of you. I have PTSD."