Mixing is when an engineer carves and balances the separate tracks in a session to sound good when played together. It's the action to balance all the tracks, reduce clashes between instruments, tighten grooves, and emphasize important song elements with tools like EQ, compression, panning, reverb, etc to make them feel like a solid, cohesive song.

Mastering is the process of putting the finishing touches on a song by enhancing the overall sound, and if we're talking about an album, the mission is creating consistency across the album, and preparing it for distribution.