'Would like to' is most often used to say politely what you want or what someone else wants. 'I would like to go now.' It is also used to invite someone to do something. 'Would you like to have dinner with me?' 'Wish' can be synonymous with 'would like to' in expressing 'want' in a more formal way. 'You may look around, if you wish.' It is also used to express longing or desire for something that is unlikely to happen. 'I wish I were rich' and to say you feel sorry or disappointed about something you did or did not do. 'I wish I had never come'.

"I would like to" signals the intention to do something. eg. I would like to eat at a fancy restaurant when i get the chance. I would like to have a cheeseburger and fries. (When ordering at McDonald's) "I wish" does not need to have any practical grounds and more often than not, have no possibility of happening. There is no intention of doing anything to make this come to pass. eg. I wish i had superpowers. I wish I was young again. Hope this helped.

The difference is in the grammar. 1. I would like you to refer to a dictionary. 2. I wish you would refer to a dictionary. Now go and study that.

There really isn't much of a difference between the two. You say 'i like to' when you are expressing a wish so it is almost the same thing.