I use the term "master" you prefer source-let's agree there is an original tape of the recording and leave it at that.
No. There isn't A tape. There are multiple tapes, multiple tracks, and multiple takes. Remember, for the vast majority of records made in the last 40 years, there was no original performance. Records are made in pieces, with a rhythm track here, and a lead vocal track there. Nobody in the business calls these "masters." (I'll agree that many uninformed consumers do, but that reflects their misconceptions about recording generally.)
The job of mastering largely involves taking all these parts and deciding which channel or channels they should go in and how loud they should be in each channel. That's called mixing. Every master is mixed (at least in the pop music world).
Remastering involves going back to those original tapes and remixing them in a different way. That's why EVERY remaster is remixed--practically by definition. Remastering is not just about "cleaning up the tapes and preserving everything else." It's about making a different master. Sometimes that master sounds very close to the original release, and sometimes not.