Yes they are similar, but...
When you want to say that it is required something to be done regularly you use have to
He has to do his homework after school every day. |
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Cf. however
1. You must take three of these pills every day after lunch.
Formally, when you speak about the law or obligation you use must
Everyone must pay taxes. |
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Cf.
2. I have to send in my tax return before 31st January.
3. Not pay tax? Of course you have to pay tax! Everyone has to pay tax.
I don't have to go to school = there is no need for me to go to school
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Also = "There is no obligation for me to go to school", e.g.
4. I don't have to go to school. I'm 16 now.
If you believe in certain fact you use must
You must be that man from the TV.
(If you believe something is not true you say You can't be the man from the TV.)
You use have to with the similar meaning but not with you It has to be true.
(negative: It can’t be true.)
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Cf.
5. You have to be joking.
MrP