Mixing is the process of taking individual recorded tracks and blending them into what is considered "the song". The idea is to allow all instruments, vocals, and other assorted noises to be clearly heard in accordance with the "vision" of the artist. Tonal balances (eq, volume levels) are decided at this stage to the best ability of the engineer. If the intention is to send it off for further mastering, the mixing process can end there.
The mastering process then continues where mixing left off to handle song by song compression levels, volume balances between songs, overall sweetening with additional EQ, all done by "golden eared" mastering engineers with state-of-the-art mastering equipment (and that DOESN'T necessarily mean the TC Electronic Finalizer!!!).
In short, mixing does the blending into what is considered the final song layout/structure of the tracks, mastering is the polish/waxing of the final mixes into a cohesive, professional-sounding product.
(Kinda like waxing the apples at the grocery store before selling them - the apples were good before, but they're even more appealing after a nice "sheen" has been applied!)
Regardless of the marketing hype surrounding these so-called mastering processors - simply putting them in the signal chain on your final mix doesn't mean you've "mastered" your track... the actual process is FAR MORE involved than that, bordering on being an artform in itself.
Bruce Valeriani
Blue Bear Sound