The contracted form of ‘will not’ is “won’t” and the contracted form of ‘shall not’ is “shan’t”. The verbs ‘will’ and ‘shall’ are most often used in their short form with an apostrophe, e.g. I will = I’ll; She will = she’ll; they will = they’ll, and I shall = I’ll; he shall = he’ll; we shall = we’ll; therefore, the fundamental difference between ‘will’ and ‘shall’ is not given very much importance these days.  However, there is no harm in having a quick look at the difference:

Shall

“Shall” with the First Person subject of a sentence expresses ‘simple futurity’; with the Second Person and Third Person, it may express a command, promise, threat, determination, etc.

e.g.  I shall go at once.  [ I – First Person — simple futurity]

You shall go at once.  [you – Second Person – a command]

He shall be dismissed for negligence of duty.  [He – Third Person – a threat]

You all shall get some reward if you work hard.  [you – Second Person – a promise.]

Will

“Will” with the Second and Third Person subject of a sentence expresses ‘simple futurity’; with the First Person, it expresses determination, threat, willingness, etc.

These two rules are not given much importance these days because we use  ’ll, the contracted form of either ‘will’ or ‘shall’.

And there is little difference if it is ‘shall’ or ‘will’.  For example, “He’ll meet us at the airport.” in this sentence “He’ll” can be ‘He will’ or ‘He shall’.

When we actually want to show the difference, we use the word ‘will’ or ‘shall’ in full or rephrase the entire sentence to give us the desired meaning.