Hello Libby,
If you hope for something, you want it to be true or to happen, and you usually believe that it is possible or likely.
"He hopes to get this job within 2 weeks."
Here he is anticipating to get it and waiting for it to come true.He did what it takes and expects the good results.
On the other hand If you wish something were true, you would like it to be true, even though you know that it is impossible or unlikely.
" He wishes,he could do that..."
Here it is a desire to do and achieve that, yet it is quite impossible or unlikely to happen.