You use "might have" to express a possibilty. But you use "must have" to show confidence in something, as if you are sure about something.

Might is also a bit more polite. Even if you know he committed a mistake, you can use the word 'might' to sound less harsh. So, you see someone made a mistake and you say "you might have made a mistake there". That comes off as politer than 'you made a mistake' or "you must have made a mistake". Either way he knows he made a mistake.

Agree with 一 might have - 50% certain must have - 90%-100% certain

^ he's right

The tones. Kind of certain vs. absolutely certain.