Music was cut from iTunes to iPhone, not copied...

I thought I synced my iPhone and Mac iTunes. Then I thought I followed the right steps to copy files from iTunes on my Mac to my iPhone. What resulted was a moving of the files. I now have albums such that part of the music is on my phone and the remaineder still sits on my Mac. First, how do I move all my songs back to my Mac. Second, how then do I copy complete albums or selections of songs onto my iPhone. Before I was dragging entire albums but for some reason only part of the content was being transferred.