MUST VS. HAVE TO

 Both must and have to (have got to) are used to express obligation or necessity.

Obligation is a moral or legal duty to do something. If you have an obligation to do something, it means you required (зобов’язаний) to do this. For example, Parents have an obligation to educate their children. The government has a legal obligation to help poor people. 

Necessity is something you need to do, something you can’t escape. For example, Sewing is something I do because of necessity, not for pleasure.

Must, have to and have got to

are tree forms that can be used interchangeably in the present tense. However, there are differences between them. When used in the first person, have to and have got to suggest that the obligation comes from someone else (law, our boss at work, parents etc.) not us. On the contrary, must suggests that it is the speaker who has decided that something is necessary and he believes it’s the right thing to do. 

•  I must clean the house before mum gets back. I want her to find it all neat and tidy. (this is my personal will – особисте бажання)
• Sorry, I can't come out now. I've got to/have to tidy up my room before I'm allowed out. (This is my parents’ order – наказ батьків, but I have no choice).

Have got to is characteristic of very informal speech. Have to sounds slightly more formal.

 Have to and have got to are interchangeable for single actions:

I have to/have got to check the oil level in the car.

 But when we talk about repeated obligations, HAVE TO is preferable:

I often have to get up at 5.

Do you ever have to get up at 5?  

 In other persons (you, he, she etc.) must is stronger than have to and can indicate stress or urgency – вказувати на тиск чи невідкладність.

 You must phone home at once. It's urgent.

They must do something about it.

There is a nice poem about farmers and their obligations.

Just a Farmer

"Just a Farmer", you said
And I laughed 'cause I knew
All the things that farmers
Must be able to do.

They must study the land,
Then watch the sky
And figure just when
Is the right time and why -

To sow and to plant
To buy and to sell
To go to the market
With cattle and well -

You know the books
That farmers must keep
To pay all those taxes
And be able to sleep.

And you know the fixing
That farmers must do
When machines like mad monsters
Blow a gasket or two.

I guess when God needed
Folks to care for His earth
He chose "just farmers"
'Cause He knew their true worth.

Must is also used in pressing invitations, such as: You really must come and see us some time and in emphatic advice, such as: You really must take a holiday this year.

Must (not have to or have got to) is used in public notices or documents expressing commands:

Guests must sign in at the desk.
Candidates must choose five questions.

With frequency adverbs such as always, often, sometimes, never, etc, have to is normally preferred:

I usually have to work on Saturdays so I hardly ever go away for the weekend.
They sometimes have to get their own suppers if their mother is working late.

FORM

Must and have got to have no future or past tense forms. They are used only in present tense form. We cannot say: I had got to.../ I'll have got to.../ I'll must.../ I've must....

Have to is the only one of the three that possesses past and future forms. 

Future

We had to leave the party early. Tom was obviously unwell.

I'll have to speak to him.

QUESTIONS

 Questions with have to and have got to are more common especially when the obligation came from the outside:

What time have you got to be back?

How often do you have to travel to America on business?

Questions with must are unusual, but possible:

Must you leave right now? Won't you stay a little longer?

Must I go to school today?

 We generally prefer Must you…? to Do you have to…?/Have you got  to…? to mean 'Can't you stop yourself...?'

Must you always interrupt me when I'm speaking?

NEGATIVES

As you can see, the differences between the present forms are sometimes very small. However, there is a huge difference in the negative forms.

We use 'mustn't' to express strong obligations NOT to do something:

• We mustn't talk about it. It's confidential.
• I mustn't eat chocolate. It's bad for me.
• You mustn't phone me at work. We aren't allowed personal calls.