Usamos must, have to, need to, mustn't, don't have to para falar de obrigação, necessidade e proibição.
You must show your passport at the border. (obrigação — regra)
I have to finish this report today. (obrigação externa)
You mustn't use your phone during the exam. (proibição)
You don't have to come if you're busy. (sem obrigação)
Must = obrigação interna (o falante impõe); have to = obrigação externa (regra, lei, outra pessoa impõe).
I must call my mum — I haven't spoken to her in a week. (decisão própria)
You have to wear a helmet when cycling on public roads. (lei)
She must be more careful. (o falante decide/aconselha fortemente)
He has to work on Saturdays. (o empregador exige)
Esta distinção é crítica: mustn't = proibição (é proibido fazê-lo). Don't have to = sem obrigação (é opcional — pode fazer se quiser).
You mustn't park here — it's illegal. (PROIBIDO)
You don't have to wear a tie — it's a casual event. (OPCIONAL)
Patients mustn't eat before surgery.
You don't have to bring food — there'll be plenty.
A distinção mustn't vs. don't have to é o erro mais comum: