Do you know your modal verbs?

um ano atrás

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?