So what is the difference between "you have to do this" and "you must do this"? Don't they mean the same?
Same goes with "he may be in the library" and "he might be in the library". I'm kind of confused on which one to use in above's context.
So what is the difference between "you have to do this" and "you must do this"? Don't they mean the same?
Same goes with "he may be in the library" and "he might be in the library". I'm kind of confused on which one to use in above's context.
While the terms are indeed quite similar in meaning, they have different connotations (feelings).
Saying have to seems less required than must because must tends to be used more in formal settings.
In your example, may and might are also quite close in meaning. They do express slightly different degrees of certainty, though. May generally indicates a higher likelihood than might. If "he may be in the library," that could probably be a good place to start looking for him. If "he might be in the library," that implies you're more unsure about his whereabouts.
This article from Masterclass (warning: video autoplay on that site) explains might vs. may pretty well. https://www.masterclass.com/articles/may-vs-might-explained
It also clarifies the important distinction that may is used to indicate permission as well as probability. "May I have a moment of your time?" is the much more common way to ask permission in American English, at least. If I hear, "Might I have a moment of your time?" it feels more stuffy and formal or more British to my American ears.