Understanding the Use of Modal Verbs in English

I have difficulty using modal verbs in English such as must, have to, should and ought to. I especially get confused about when to use one and when to use the other and how to convey shades of meaning correctly. Can anyone explain the difference between these verbs in detail and give examples of how to use them in context? This will help me better understand how to choose the right modal verb in different situations.

It wasn't easy to figure out modal verbs, but I found a simple pattern for myself. Must expresses a strict necessity: "You must wear a seatbelt" (you need to buckle up - this is a rule). Have to conveys an obligation, but from the side of external circumstances: "I have to wake up early for work" (I need to get up early because of work). Should is used to give advice: "You should eat more vegetables" (you should eat more vegetables)). Ought to is also advice, but more formal: "You ought to apologize" (you should apologize). To understand it more deeply, I recommend learn english grammar with promova - it has explanations with examples that immediately help you grasp the difference.