Translation:Everybody usually has dreams while they are sleeping.
It is said that "giấc mơ =/ ước mơ", but why?
giấc mơ is the sleeping dream and ước mơ is the living dream?
What you said above is quite correct. "giấc mơ" refers to a dream occurred while you sleep. On the other hand, "ước mơ" (ước = to wish) refers to the dream that you wish to come true.