Modal auxiliary verbs mush, have to and should all can be used to express obligation or necessity to do something. But there are slight yet clear differences among them. Simply just keep in brain that must is mainly used in formal, written and also personal context while have to is used mainly in spoken English, situational context. Simply Must is used from personal context and have to from situational context not personal. And the modal verb should is mainly used to express advice or opinion. However, must and have to can also be used to express opinion or advice. But must is more stronger or emphatic than have to or should . And to give negative opinion, only shouldn’t can be used. Again, all three modal verbs are used to express probability or certainty.
To get better understanding on the differences among these 3 modal verbs, please watch this video. Please note that there are slight differences among these 3 verbs. So you have to get those properly to avoid mistakes. In order to get the knowledge from the video into the head, please practice constantly. If you really find this video helpful then share it with friends. Good luck!