Updated: Oct 15, 2021
In 1611 English, and in fact for many long years afterward, those two words were not synonymous. I was once in a court of law where the meaning of "shall" as quoted in a law was disputed. It was proven that the State Supreme Court had already reluctantly conceded that even though those two words had once carried specific meanings not interchangeable with each other, the general sloppiness of modern English usage had rendered those differences moot.
To say that we shall or shall not do something is an imperative. It must or must not be done. To say that we will or will not do something communicates our desire. I don't do everything that I will to do. Sometimes circumstances prevent me. A good example of this in the word of God is I Timothy 2:3-4, For this is good and acceptable in the sight of God our Saviour; Who will have all men to be saved, and to come unto the knowledge of the truth. Do all men come to the knowledge of the truth? Obviously not. We are told of God's desire, not what will happen.
Now I know that this will turn Calvinists inside out. Their God is not big enough to grant sinners free will and still bring all prophecy to fruition. They will frankly tell you that they cannot conceive of a God that is not absolutely sovereign in every little detail. The idea that God might desire something and then not get what he wants is beyond their comprehension. It never occurs to them that a God who they can conceive is far too small.
O Jerusalem, Jerusalem, which killest the prophets, and stonest them that are sent unto thee; how often would I have gathered thy children together, as a hen doth gather her brood under her wings, and ye would not! Luke 13:34. We see the usage of the word "would" which is past tense of "will". Jesus, who is God wanted one thing. Jerusalem which is composed of men, wanted another thing. The will of man prevailed over the will of God.
Calvinists have an answer for that. They say that it was the will of Jesus's flesh that was expressed. They do not see his flesh as God. Calvin had Servitus burned at the stake over that issue. Read his notes on John 1:14 if you don't believe that. The Apostle John certainly believed that the flesh of Jesus Christ is God. That which was from the beginning, which we have heard, which we have seen with our eyes, which we have looked upon, and our hands have handled, of the Word of life, I John 1:1.
Whatever it was that John saw and whatever it was that he touched had been from the beginning. He didn't touch his soul and he didn't touch his spirit. He touched and saw his flesh. The Word was made flesh, John 1:14; not put into flesh as many picture the deity of Jesus Christ. Jesus Christ is [the fulness of the Godhead bodily] Colossians 2:9. God desired that Jerusalem be gathered unto him and Jerusalem desired otherwise. Jerusalem's will prevailed.
When the word "shall" is used you can bank on it. Wherefore, sirs, be of good cheer: for I believe God, that it shall be even as it was told me, Acts 27:25. Here Paul has no doubt. "It shall be" makes it clear that everything God said will come to pass. Shall and will are not interchangeable words. God reveals himself through his word, not through the reasoning of men. A study of those two words demonstrates the true strength and power of our God and distinguishes him from the peanut god of John Calvin.