may have meant & might have meant

[E2e4]

I came across this sentence on this forum.

I can't figure out what they may have meant when they were talking about "tissue". You must have misheard it.

Please explain to me when we usually use "may have meant" and when we use "might have meant" and what is the difference between them.

Thanks

[Mister Micawber]

There is no difference in meaning of the two 'present perfect' forms (which are actually past tenses of those auxiliaries). In simple tenses, they can also be synonymous, or 'might' can be the past of 'may' (as in reported speech).
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Native English teacher at Mister Micawber's

[Atomos]

Hi E2e4,

If I remember correctly, 'may' and 'might' are different in their levels of possibility. That is 'may' is slightly more sure (50% chance) while 'might' expresses more doubt (20-30% chance).
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"I would rather be hated for who I am, than loved for who I am not." Kurt Cobain

[Mister Micawber]

I'm afraid that is not really true, Atomos. That is one of those prescriptions cooked up for convenience' sake. In reality, native use depends more on individual habit.
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Native English teacher at Mister Micawber's

[Bookaholic_English]

Yes, that's not really true. But I'm afraid that the difference is necessary in our written tests.
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Rolling stone gathers no moss.

[Mister Micawber]

Can you show me a written test where 'may' vs 'might' is tested other than in reported speech or another present vs past structure?
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Native English teacher at Mister Micawber's