Shall, Will and Must, in everyday usage are used with varying degrees of interchange, whether correctly is another matter. In writing contracts, or at least the ones that I was involved in, it was quite important to use the right word of the three.
Before I retired I was involved in quite a few projects of varying values up to multimillions £ and as the client's representative on these projects it was vital that the correct words were used. Whenever one wanted to ensure that the contractor was contractually liable to do what you wanted him to do one always used 'shall' and never 'will' or must'. So for example one would write that 'the contractor shall repaint all the pipework every five years' not that he 'will' or must'. However, if the contract referred to what the client was going to do then one always used 'will' as in 'OPA [the organisation I worked for] will provide the contractor with a complete set of drawings within 28 days of the start of the contract'. This meant that OPA was not contractually bound to do what was stated in the contract in the way that the contractor was. Must, however, was never be used in contracts, or at least it was never used if the person writing it knew what he was doing.
Tim