Time Machine quirk/bug? – Create New Backup, or Inherit Backup History

I treasure this community, and strive to not post regarding a topic I can learn about from FAQs and the like, but this remains vexing. Admire and am well-acquainted with Pondini.org and others, but believe confusion arises over ambiguity in the simplest of terms –– in my case, under just precisely which circumstances is "a different computer" actually, truly, "a different computer". I am gaining the impression that sometimes TM can believe "a different computer" is in play, when actually...

Time Machine quirk/bug? – Create New Backup, or Inherit Backup History