If we gave the definitions for these words straight out of the dictionary, you would be reading a page of conditions that would hardly enlighten you. Well, for practical purposes, you really don't need to worry about vague definitions. English grammarians have been arguing for 300 years and insisting on the use of shall with the first person and use of will with the second and third person to express the simple future. That would mean that I shall be able to see her tomorrow , but you , she , and he will be able to see her tomorrow .
Few experts bother with the argument any more, mostly because no one is paying attention.
Shall has almost passed out of the American language, in speech and in print. Will is used for all purposes and is not considered substandard. It's a first-class example of a lovely theory killed by a fact. American usage all but ignores shall today, except for legal language, for example, Leasing agents shall provide proper fire equipment and Plaintiffs shall submit statements, etc. The distinctions that grammarians used to promote for will and shall appear to be characteristic of English as it is, or was, spoken in the south of England.