Well Matt there must be more educated people on this subject than me but here's my understanding.
Typically each mike in the studio is linked to a strata of 3/4 inch tape through the mixing desk and is laid down as a single track. These tracks can be adjusted seperately and where necessary added to or taken away. The early 60's had artists adjusting their volume by how hfar away from the mike they were then 4 track, 8 track, 16 track recordings came on stream.
The master tape is then used to cut an acteate to check sound quality and maybe if the recording has been done with a studio artist employed by the writer it can be hawked around to publishers, established artists, record labels etc in an attempt to sell or gain work. There is apparently or indeed was an Acetate of Van McCoy doing 'You Gonna Make Me Love You' which he used to demonstrate how the record should be performed before it was redone by Sandi Shelton (That may be an urban myth though)
If it is cut by the label and they are happy with the sound it then is sent to the pressing plant where two 'mother plates' are produced one for each side. These kind of reverse the playing of a 45 in that the sound is input and a lathe then cuts the track into a metal plate. These are the pressing plates and are like a negative of the 45 and include the obviously reversed matrix details and all dead wax detail. You can even play these if you reverse your deck though few survive as they were usualy recycled often being made of copper.
These mother plates often called 'stampers' are what the pressing plant use to press the vinyl or styrene with the labels being added at the same time.
Often different mixes made their way to either different pressing plants or the same plant where multiple presses were used just purely as the acetate was cut with a different mix from the master tape. There mother plates were not everlasting obviously so on big runs purther plates may have needed to be produced and often these new plates would have the matrix detail ammended slightly.
It is the master tapes that now allow us to hear just the vocals or just the instrumentals as we heard when Pete Smith posted some motown stuff some months back.
I saw some years ago a guy who had bought some rock and roll 78's in Memphis and the store had used some old stampers to pack them in for his journey back to the UK. These then turned out to be the stampers for two of Elvis' Sun 78's which he auctioned via Sotherbys for serveral £,000.
Sure others can correct or add detail.