"I wish" implies that you doubt that something you want will happen, or that something did not happen the way you wanted it to. For example, "I wish I could get a full-ride scholarship for attending MIT," or "I wish that I got an A on my final exam." Hope implies that something you want to happen is still a possibility, even if it happened in the past (and you do not know the results). To reuse one of the previous examples twice, "I hope I got an A on my final exam," or "I hope that I get an A on my final exam".

"I wish to" can mean the same "I want to" but it is much more formal。 “I wish to”的意思是相同于“我想要”，但它更正式。 例句：I wish to make a complaint. 我想要提出申诉。 I wish to see the manager. 我想要见经理。 You can also use "wish" with a noun to offer good wishes'. 你可以连同"wish" 和一个名词一起使用来祝愿别人。 例句：I wish you all the best in your new job.　我祝你能在新的工作中顺顺利利。 　　　We wish you a merry Christmas. 我们祝你圣诞快乐。 注意：用Hope的分别就在这里了。^_^ When you want to offer good wishes using a verb, you must use "hope" not "wish". 当你要用动词祝愿别人时，一定要用 "hope". 例句： We wish you the best of luck. Vs We hope you have the best of luck. I wish you a safe and pleasant journey. Vs I hope you have a safe and pleasant journey 希望能帮到你。

Yes - wish is about the impossible! I wish I were younger, I wish I were more handsome 不可能的 Hope - is about the possible 有可能的 I hope it is sunny tomorrow. Not easy to distinguish in Chinese there is only 希望 in common use

I hope you have great time on your vacation! I know you are getting married on this coming weekend but I can't able to make it. But I wish you to have the best of lucky on your wedding.