Hope means something which is possible and probable.
Wish means something which is not likely to happen or something which is impossible.
We use 'hope' to express a wish/desire/aspiration that has a good chance of being true.
• I hope you will be successful.
• We hope the phone lines are clear next Saturday.
• We all hope that we will find happiness.
• We hope the weather will be good tomorrow.
We use 'wish' to express a hope/desire/aspiration that seems to be unlikely or even impossible (i.e. not much chance or even zero chance)
• I wish I were taller.
• I wish I were smarter.
• We wish the phone lines were always clear.
• You wish you were richer.
• Everyone wishes for world peace.
There is one more use for the word "wish".......wish = desire
For example, the usual wish spoken at special times, e.g.,
I wish you a Merry Christmas !.. that means: My desire is that you have a merry Christmas!
- We wish you a happy birthday!..that means: Our desire is that you have a happy birthday.
- I wish he would get better...that means: My desire is that he gets well. He doesn’t feel well now and my strong desire is that he gets better soon.
- I wish you all the best / I wish you good luck...that means: My desire is that you will have good luck in the future.