As a general rule, "wish" refers to things that are unlikely to happen.  "Hope" refers to things that could happen.

"I wish you would clean your room" (But I know you won't.)

"I hope he finishes cleaning his room before the bus arrives" (It might happen.)

"I wish I could fly around the world" (But it's never going to happen.)

"I hope I can go to Italy this summer" (I have enough money and can get time off, so it could happen)

But in casual English, they mean the same thing.

I hope is when u want something to happen usually when that something is realistic. For an example: I hope I will pass my test. I wish is also when u want something to happen but this is usually said when there is a low chance of this thing happening. For example: I wish humans could fly.

What an excellent question!

Your explanations are great too ^^

Thank you Grace n Brooke very much :)