The difference between will and shall depends, to a certain extent, on context.

Proper use of will always conveys mere intent. Shall conveys compulsion. In contract areas, in software requirements language, and certain other venues, using will means that the goal or intent is strongly desired, but you might still get paid if you just get close, or talk to the customer.

Shall, in a contract sense, often means part of the contract isn’t met – and often the contract price is adjusted accordingly.

In certain contexts the difference between will and shall is pretty serious.

When you state you shall climb the mountain, you imply that your mind, your intent, cannot be changed. That is, you apply a compulsion on yourself to climb the mountain. Stating an intent to climb the mountain, that you will climb it, instead acknowledges other factors might override your choice, such as weather, family illness or mishap, injury, or a chance to drive the first space ship to Mars an back, carrying Mel Brooks, Rick Moranis, Joan Rivers, and Bill Pullman (from Spaceballs, 1987). Or a gift certificate for five pounds of (very good) chocolate.

In casual conversation and informal usage, the difference between intending an action, will, and being compelled to act, shall, is often overlooked. That doesn’t change the proper usage, nor address the contactual, formal implications.

”Will can imply volition or intention, while shall can imply necessity:
I will scale Mount Everest. (”and no one can stop me!”)
You shall take the garbage out before you do anything else. (”You have no choice, Junior!”)

If instead you replaced the wills with shalls and vice versa, the meaning implied by the constructions would be exactly the same.

“I will scale Mount Everest”. “I shall scale Mount Everest”. I see no difference in meaning. Both imply an intent to climb the mount.

“You shall take the garbage out”. “You will take the garbage out”. Both imply an unarguable instruction to take the garbage out.