"My fault." and "My mistake."
What's the difference between the two expressions? They are similar, but I kind of sense that there is still some slight difference between them that I can tell clearly.Thanks for your help!

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Answer

If you say something is your fault, you take responsibility for what happened. It's my fault the car won't start. I left the the door ajar and the battery died. Saying "my mistake" usually just acknowledges an error. Suppose I greet someone by name and then realize I said the wrong name or mistook them for someone else. I could say, "Sorry, my mistake."