Just before dawn

Early this morning ("just as the sun was rising, I heard ...."). I noticed that although it looked like a good sunrise, the moon was still in the east. I don't really know just how the sun and moon move relative to each other; of course the earth is rotating all the time, but the relative motions are not clear to me. I think what prompted all this is that often I can see the moon in the west at dawn and here it is still in the east.

Now, someone is going to come up with little diagrams to demonstrate all this and I may be more confused than ever!

Very windy today! Blowing the moon around?