Throw the word engineer away -- that's just whoever is doing the work.

mastering: Here are some good definitions I've found:
(a) Audio mastering: "...is the process of preparing and transferring recorded audio from a source containing the final mix to a data storage device (the master); the source from which all copies will be produced"
(b) "The last transfer from work in progress to finished product that is intended for the end consumer."
(c)"a process whereby a number of songs, after being mixed down, are EQ'd, compressed as necessary, and balanced in volume with each other, so that they will sound good when placed together on a CD."

Basically mastering is always done to the finished stereo file. Can you use EQ and compression to overcome a less than stellar mix? I guess so, but that seems like a self defeating task.

Mixing: This is what all of us do (ha, ha). We take our 4, 8, 12, 24 ... tracks and individually pan them, eq them, compress them, reverb them, and (optionally) send them to mix busses as groups to process them there (eq, compression, effects) so that we get a nice, balanced sounding stereo master output. If we have done our jobs well, we can take our stereo mix out to the car, over to a friend's house, put it on a mp3 player, etc. and it will pretty much sound the same (within reason) as what we heard in our "studio". If they sound too different on different systems, it is back to the DAW and re-mix a little. The key to good mixing is "trusting what your hear".

I have an untreated room, BX5a 5" monitors and ath-m50 headphones. I listen under everything, listen to reference tracks (commercial CD's I think are great) and do the best I can. I can't seem to get a good mix without listening on other systems though -- my listening setup is not that good, I guess. Is it magic ears??? Nope -- I can get the mix to sound pretty decent on my setup. It just doesn't "translate" to other systems like I would hope. My ears are "OK", it just means my room and my monitors (and headphones) are not re-producing the full EQ spectrum accurately enough.

Now, if I can't Mix accurately enough, how in the world could I ever hope to master accurately?

Now at bandcamp: Crows Say Vee-Eh @ bandcamp or soundcloud: Kevin @ soundcloud