wish versus hope

wish

a)I wish to  make a complaint = I want to make a complaint. (more formal)
b)Sometimes wish is used in greeting and expressions of goodwill:
I wish you all the best in your new job.
I wish you a safe flight. (= I hope you a safe flight)
I wish you a happy birthday.
c) Wish is most commonly used in hypothetical (or imagined) situations:

I wish that I had a dog. (I don't really have a dog, but if I did, I would be happy.) I wish (that) you were here. (Unfortunately, you're not, and I miss you.)

I wish I were rich.
He wishes he lived in Paris.
He never helps me with the dishes. I wish he would.
I've eaten too much. I wish I hadn't.

hope

Hope can also be used in expressions of goodwill, but the grammar is slightly different:

I hope (that) you have a Merry Christmas. I hope (that) you had a nice Birthday.

(some time in the future) (some time in the past)

I hope you a safe flight
The strike begins tomorrow. I  hope the buses will still be running.
Hope can be used to specify a desired outcome. For future hopes, the possibilities remain open, but for past hopes, the outcome has usually been determined already.

I hope you can come to the party on Saturday. I was hoping that you would come to the party. I had hoped to see you at the party on Saturday.I hope to get an A on the exam. I hope it doesn't rain tomorrow. He hopes to be elected President. She hoped you wouldn't find her.

(future possibility) (but you didn't make it) (but I didn't)(it is still possible) (although it might) (it could happen) (but you probably did)

Wish and hope are also used in certain types of requests and pleasantries.
In such situations, wish carries a more definite and formal tone.

I wish to see the doctor.I hope to see you again.

(right now)(anytime in the future)

notes: When the meanings is the same, We use wish for  present and past tense, and hope for the future.