"Wish" is used not only for regrets but also for best wishes. When you want to send your best, pray or petition to somebody, you can use it too. For example: "I wish you success with your new school" or "I wish you all the best". But when you talk about regrets, you say: "I wish you were here" or "I wish he could come". You can use "If only" here. It has the same meaning. I hope this will help you :)

A "wish" is something that a) isn't true, that b) you want. It could be in the future. It could be a thing that hasn't happened yet. I have no coffee now. I want coffee. "I wish someone would bring me a cup of coffee." My wife brings me coffee. "My wish came true." It could be in the past. "I wish I had remembered to bring my umbrella!" Since it's in the past, it can't be changed. It can't "come true." The good thing you want ISN'T true. The thing that happened was something you DIDN'T want. So, it is expressing regret. When you say what you want--out loud, or silently in your head--you are "making a wish." The phrase "I wish you a Merry Christmas," it means "I am making a wish. My wish is for you to have a Merry Christmas." In the United States, when children see a bright star (usually it's really the PLANET Venus!) they say: "Star light Star bright First star I see tonight I wish I may I wish I might Have the wish I make tonight." Then they close their eyes and wish for something.

It depends on whether 'wish' is followed by a noun or a verb. - If it is followed by a noun, it is the equivalent of the French word 'souhaiter'. For example you can say 'I wish you a happy birthday', or 'I wished him good luck'. - If it is followed by a verb, it can express a regret, or simply a desire for something to be different. For example a poor person might say 'I wish I had more money'. A fat person might say 'I wish I were thin'. Or if you are tired in the morning, you might say 'I wish I hadn't gone to bed so late.' I hope this helps. Please ask if anything isn't clear.