HAVE TO, MUST & SHOULD are verbs which we use for obligation and recommendations.
Use SHOULD to make a recommendation (i.e. when you think it is a good idea for someone to do something). Example: You should do some grammar exercises to improve your English. 2. You should drink 6 glasses of water a day.
Use HAVE TO for laws or strong external obligation. Example: You have to wear a seat belt when driving. 2. In my country, you have to be 16 years old to buy cigarettes. Note that the negative of have to is mustn’t, can’t or not be allowed to. For example: You mustn’t drink and drive. 2. You can’t smoke in restaurants in Malta. 3. We aren’t allowed to use our phones in class.
HAVE GOT TO is used in the same way as HAVE TO. The only difference is that it is less formal so it is more common in speaking.
Use DON’T HAVE TO for things that aren’t necessary or you don’t need to do. For example: You don’t have to pay for children under the age of 6. 2. We don’t have to do any schoolwork in the summer holidays.
Use MUST for personal obligation. Example: I must study for my exam tomorrow. 2. I must eat less ice-cream! I’m getting fat.
Note that in many situations it makes no difference if you say MUST or HAVE TO. The difference is one of degree or how strong the obligation is. For example: I have to / must get more exercise.