Original LP pressings from the 1950's, 60's, 70's, and 80's were almost never made using the "master" tape (I'm not speaking of the 1" or 2" multi-track master, but rather the 1/4" or 1/2' 2-track mixdown tape) as the source for mastering, but using instead a "production" tape. A production tape is a copy once or more removed from the original mixdown tape, the copying done so as not to endanger the precious 2-track master, which was immediately put into storage for safe keeping (along with the multi-track master). It is the production master that was played back when the mastering was done
When a modern reissue is done, it can be in a number of ways. How much research and digging through tape boxes the person/company wants to put into the project varies---a lot. Time is money, and major labels like to minimize the amount of money they spend to create product. In contrast, the best reissue record company's are known for going to extreme measures to find as early (close to the original 2-track mix tape, or even the multi-track master) a tape as possible.
An example: When Columbia Records reissued Miles Davis' Kind Of Blue on LP in the first decade of the 2000's (I believe it was), they used a digital copy of the 2-track mix tape as their source for mastering, creating a new "father" for the plating process from that digital tape. Compare that with what audiophile reissue company Classic Records did back in 1997:
Classic owner Mike Hobson paid for the rights to issue Kind Of Blue on LP, and was granted access to all the KOB tapes Sony (who owns Columbia records) had. He and his team---including the well-known master of mastering, Bernie Grundman---obtained them ALL. Not just the production master, not just the original 2-track mixdown tape, but the original 3-track master---THE tape that was made as Miles and his band played.
In listening to all the tapes, Michael and Bernie finally discovered why two of the songs had always been heard slightly off key and playing at the wrong speed: on the first day of the KOB sessions, the recorder was running at the wrong speed! A different machine was used on subsequent sessions, and that one was running at correct speed. All versions of Kind Of Blue ever issued---the original 1959 6-eye Columbia, the 8-track and cassette, and finally the CD---had two of the songs out of tune and playing at the wrong speed!
In his new mastering of KOB for it's Classic Records reissue in 1997, Bernie corrected the speed error. But he went much, much further: he didn't use the production master as his source, or even the original 2-track mixdown master. He used the original multi-track tape (only 3 tracks; this was 1959, after all) as the source for his mastering job. Classic Records had also received the original "father" made at the time of the original mastering of KOB, back in 1959, the "metal work" as it is called.
So Hobson and Grundman compared Michael's 1959 6-eye Columbia pressing of the album, the original 2-track mixdown, the 3-track master, and a new 2-track Bernie made off the father. All were compared in deciding how to proceed, and what to use as the source for the new reissue.
When doing a reissue using a multi-track master as the source, it is common practice to make a new 2-track production master and use it as the source for mastering. Hobson and Grundman---having heard the incredible sound quality of the 3-track master (unplayed since 1959!)---decided to use it as the source. But they didn't stop there in their efforts to make the Classic Records reissue the very best sounding one that was possible: rather than make a new production master from the 3-track master---the production master tape then fed into the mastering lathe to cut a new father---Grundman fed the output from the 3-track machine directly into the lathe, cutting the father directly from the 3-track master! That of course meant Bernie had to mix the 3-tracks to two, to make a stereo father. He and Hobson did the mix so as to be indistinguishable from that heard on the original 1959 LP.
But that's only half the story: we still don't have an LP, do we? Hobson---having in his hands the new father from Grundman---went about manufacturing the new Classic Records LP version Of Kind Of Blue. I COULD recount that part of the story for you (and it's sequel in the even better version by Analogue Productions---made in co-operation with and participation of both Michael Hobson and Bernie Grundman), but I don't want to put you to sleep. Or has that ship already sailed? ;-)