While a wish in its proper sense is an aspiration, a want is a need. For much of its career, a want didn't even necessarily imply a need; it meant merely a lack. (The etymologists say it's from the Old Norse for "something missing".) You might say a naked sword wanted its scabbard, or that it wanted five minutes to midnight. If it was said of a woman that she wanted a lover, it didn't mean she was anxious for one, only that she didn't have one; otherwise it would be said that she wished for one.
It's hard to say when want graduated from meaning "lack" to meaning "need" to meaning "desire". For the Elizabethans, when they said (for example) "the baby wants his mother", it could be any of those three things - or perhaps all of them at once - but today we mean that the baby actively and consciously desires to have her. When the baby gets older and says "I want to go home", the distinction between wanting and wishing disappears altogether.
Meanwhile wishes have become bolder. Peremptory, even. Supposing someone says "I wish to see you". An Elizabethan would probably have meant "I'd love to see you". A New Elizabethan means "You're to come and see me". If the chairman says he wishes to say a few words, you can be sure that he will go ahead and say them. But wishes have also become genteel. "You wish to use the toilet?" says the hostess when she thinks someone wants to go to the lavatory. It's all a bit of a muddle.Reuse content