"Dream" is for the thing that happens while you are asleep. "Daydream" is when you are awake and thinking about things in a dreamy way. A student who isn't paying attention during class might daydream while the teacher is talking. The student might think about going on an adventure in some far off place. But he is still awake. His mind is just not on the class.

you dream when you're asleep and daydream while you're not asleep.... you know... when you start thinking about something and don't even hear what happens around you... something like that :)

dream ............... when you are a sleep daydream, ............. when you are a wake

Here is a nice song called "Dream, dream, dream ," you can listen to it here http://www.dailymotion.com/video/x5gvi7_dream-dream-dream-everly-brothers_music

a dream- мечта to dream - мечтать или видеть сон. to daydream - мечтать, бывает иногда что средь бела дня задумаешься о чем-то, начнешь представлять какую нибудь ситуацию....