It's fairly rare nowadays to see "will" used as a verb by itself. Maybe if the person has a powerful mind or great influence, such as a sorcerer or king, but most of the time you'll see "will" paired with another verb to mean a future action. "To wish" just means to desire something to happen. No guarantees here.

I will go to school tomorrow--something you want to do and are certain that you can do I wish to go to school tomorrow--Maybe you can't, maybe you are sick, maybe there is no school tomorrow.