To express degrees of necessity we can use various modal verbs.
You must leave straight away.
You have [got] to leave straight away.
must is used when the necessity is dictated by the speaker’s authority. have [got] to is used when the necessity is dictated by an external force or event, which the speaker cannot control.
(doctor to patient)
You’ve got to stop smoking.
(patient to themself)
I must stop smoking.
We don’t have to pay to get in.
We have not got to see the boss after all.
We needn’t stay late.
In all these examples there is an optional element, which defeats somewhat the element of necessity, i.e. we needn’t stay late but we can if we want to.
You ought to call your mother.
You should call your mother
These show that calling your mother is the right thing to do. There is no real difference between ought to and should, but ought to is perhaps a little stronger.
You needn’t come with us.
You mustn’t come with us.
We use needn’t to show an action is optional – I can do it if I want to. We use mustn’t to say an action is forbidden – I have no choice.