I usually say I "wish" for something if it is difficult or impossible to obtain: "I wish I lived in a mansion." "I wish I was at the beach instead of at work." "I wish I had an ice cream right now." You can also use "wish" for desiring something to occur or not occur: "I wish the war was over." "I wish this night would never end." "I wish you'd stop talking." All of these wishes indicate something that you want, but are maybe unlikely to occur when you would like it to occur. But you could also use the word "want " in these examples: "I want to live in a mansion." "I want you to stop talking." "I don't want this night to ever end." But usually I use the word "want" when I am indicating a decision I am making or thinking about something I'd like to do or obtain: "I want soup and salad, please." "I want to buy a russian grammar book." "I want to go to sleep now."

It's actually the opposite. Want expresses a stronger desire than wish, in the way that it is more direct and straightforward, whilst wish is a bit more passive. E.G. 1. I wish he'd stop tapping on the window versus 2. I want him to stop tapping on the window In these cases, you can see that wish is a more passive and hesitant than 'want'.