dream and wish

What's the difference between a dream and a wish? Many people often think that dream is synonymous with wish. I myself found nothing different when I was asked to distinguish one from the other.

My friend told me that her teacher told her this:

"A dream and a wish pertain to hoping to get or to achieve something you want, but the similarities end there... To dream is personally doing something you aim. To wish is waiting for someone to do it for you."

So do you dream or do you wish?