"Hope" usually implies something that might happen. "I hope we win the game." "I hope I get the job." Wish usually implies something that you don't expect to happen. "I wish I had a million dollars." "I wish I could fly." "I wish I could play guitar." Note that you might expect to learn to play guitar, but you know that you can't play it RIGHT NOW. ALSO: See how the tense changes between hope and wish. "I hope that I CAN see you tonight." vs. "I wish that I COULD see you tonight."

"Hope" and "wish" are synonyms, i.e. both words mean essentially the same thing and can be used interchangeably. You really can't distinguish between them.