they mean the same thing but have to can be less formal while must is generally used in a command type of situation. Have to is a more versatile while must would sound weird in a less commanding context.
1) I was given this apple but i dont know what to do with it
oh, you have to give it to the horse.
2) I don't want to do what to do that
have to could be used in both the examples so you could change "you must!" to "you have to!" and it wouldn't sound odd. But using must in the first example would sound odd. your just pointing out what you know rather than giving a command or making a strong point. At least thats how Americans typically use it. i would say you can simply use have to most of the time and it wont sound odd.