Mixing, is the Engineer’s job
he set the controls, during the original recording

Compressing, can be done at any stage, during recording, or during the mastering.
It’s done the keep the volume relatively consistent
(keep out the "peaks")

mastering, is the final editing of the song,
when they do the final mixing of the tracks, down to stereo

each is an art unto it’s own
and not that easy to learn

which is why I am so "anti" stealing music
if people really knew how hard these people work
they wouldn’t expect everything "fer freeee"
References :