Do you know your modal verbs?

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Must Not (mustn't) vs Need Not (needn't)
Can anyone tell me the difference between these two negative modal forms?
I think this is quite an advanced level question, so I would be delighted if any English language students can answer it!

 
Didn't need to vs. Needn't have
Do you know the correct way to use these 2 Modals?
What is the difference between their meanings?
Can any of the English learners out there answer this question?