[Almighty So]

Compound will have a deep cut and take care of the light scratches and swirl marks and enhance clear coat.
Polish will clear up the buff marks from the compound and protect/enhance clear coat.
Glaze will shine and protect/enhance clear coat.

Like burns said they are in order of "roughness" technically.
He mentions not waxing right away because you shouldn't buff and/or polish a brand new paint job that is still curing.