One desires something possible, the other desires something impossible or contrary to reality.
"Hope" is used when what you want is possible or realistic. "I hope it doesn't rain" = I desire that it will not rain (and it might not). The situation is achievable.
I hope it doesn't rain tomorrow.
She hopes to get the job.
We hope you enjoy your stay.
"Wish" is used when you want something impossible, unlikely, or contrary to current reality. "I wish I were taller" = I want to be taller (but I am not). It typically takes a past subjunctive.
I wish I could fly.
She wishes she had studied harder.
I wish you a happy new year.
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In formal English, "wish" is also used as a goodwill formula with no impossible or subjunctive implication: "I wish you success", "We wish you a Merry Christmas", "Best wishes." In these phrases there is nothing impossible or counterfactual, it is simply an affectionate or courteous expression. This duality of "wish" (impossible desire vs. goodwill formula) can confuse: "I wish you luck" does not imply you think they will have none; it is simply a way of saying "I hope you have luck." Context and tone always resolve the ambiguity.
Exercise 1 · Pick the right one
I _____ you a very happy birthday!
Exercise 2 · Pick the right one
I _____ the weather will be nice for our picnic tomorrow.
Exercise 3 · Form the word
'A' is used before consonant sounds; 'an' is used before vowel sounds.
'A lot of' works for countable and uncountable; 'many' only for countable; 'much' only for uncountable.
'According to' cites an external source; 'based on' indicates the evidence behind a claim.
In the active voice the subject acts; in the passive voice the subject receives the action.
Bryan López
Founder of SpeakUP Academy