We use «HOPE» for situations that are very possible and «WISH» for those that are impossible or unlikely to happen.
In terms of the form, «HOPE» is followed by the past simple to say what you hope about the past, present tense (simple/ continuous) about the present and the future although using the future form about the future is less common. See the examples:
I hope she passed all her exams last semester. (past)
I hope he’s having a good time in Moscow. (present)
I hope he enjoys his trip next month. / I hope he’ll enjoy his trip next month. (future)
As for «WISH», use the past perfect to say what you wish about the past, the past about the present, and would about the future. See the examples:
I wish he hadn’t given up. (past)
I wish I had a million dollars. (present)
I wish you would stop smoking soon. (future)
If there is a chance that something can happen, use «HOPE» instead of «WISH». To say, «I hope the director does something about the project soon» means that you think that there’s a strong possibility that the director will.