A simple defintion of the difference between have to and must -( that is except when you are using the other forms of ‘have to’ to make up for the fact that must has got parts missing) is that have to suggests external authority.
We have to use watering cans and not hosepipes at the moment because the local council says we can’t use hosepipes.
Must has the sense of internal compulsion - in other words you tell yourself that something is necessary. Following on from my pervious sentence, I could say:
I must remember to buy a watering can if I want to water my garden.
We next come to ‘ought to’ where the obligation is if you like a moral one because this is the voice of your conscience telling you the right thing to do. To continue with my gardening theme (sorry about that) I could say: I ought to put my hosepipe away as use of it is now banned but sometimes I would really like to use it at night when no one can see me!