I will go to the movie tomorrow.
I shall go to the movie tomorrow.
There is no semantic difference when shall and will are used to refer to the simple future. Will can be used in all persons.
In American English, the word shall appears in two ways: (1) we use shall in interrogative sentences asking for permission or agreement (shall we dance?) and (2) in legal documents, lawyers use shall to impose a duty (the tenant shall pay the rent each month). In this second sense, however, more enlightened lawyers are turning away from shall and using must to impose duties.