Uses of Must and Aught

Must remains unchanged whatever be its tense or the number and person of its subject. Must can refer to the present or future. And when used with the present perfect tense form of the principal verb, it can also refer to the past.

She must have gone home. (Here must is used with the present perfect of the principal verb and hence it refers to the past time.)
They must have already left. (Past)
We must discuss this matter with him. (Future)
You must meet her now. (Present)
They must pay damages. (Future)
He must be sleeping now. (Present)
You must file a petition. (Future)

Uses
Must expresses compulsion or strong obligation. It is much stronger than should.

You must admit your mistake.
They must recognize our rights.
She must quit that job.
He must complete his studies.

To express necessity

Must can express necessity.

I must get a job.
We must get up early.
We must build a strong army to defend our country.

To express probability

Must can express probability or likelihood.

That must have been a leopard.
She must have returned home now.
He must be mad to do this.
‘There is the door bell’. ‘That must be the postman.’

To express determination

Must can express strong determination.

You must insist on being given your dues.
She says that she must have her own way in the matter.

Ought

Ought was originally the past tense form of owe, but now it is used to refer to the present or future time. Ought is different from other modal auxiliaries: it is followed by an infinitive with to, while other auxiliaries are followed by an infinitive without to.

Compare:

You ought to write to her.
You must write to her.
You should write to her.
He ought to do it.
He must do it.
He should do it.

Ought is not as forceful as must, but it is stronger than should.

Uses of ought

To express duty, necessity, fitness, moral obligation etc

Ought can be used to express ideas such as duty, necessity, fitness, moral obligation etc.

We ought to help them. (Duty)
You ought to respect your teachers. (Duty or moral obligation)
He ought to be ashamed of himself. (Fitness)
We ought to move into a new home. (Necessity)
We ought to buy some furniture. (Necessity)

When ought refers to the past time, it is followed by the perfect infinitive (have + past participle). Note that this structure is used to criticize people for not doing things.

She ought to have helped me. (She didn’t help me.)
You ought to have written to her. (You didn’t write to her.)