Not necessarily the same - A copy of a VHS recording is probably not an authorized copy, however, it can be immune from action because it can be considered a "fair use exception" to copyright. So even though you may not have been specifically authorized to make a VHS copy, that's OK because it's an exception to the rule that making a copy violates copyright.
Although a company could take your money as a purchase of rights to a movie on all possible media formats, it's likely the original purchase only authorized the single purchased copy. Whether fair use would extend protection to all subsequent embodiments of a movie you purchased is questionable, and I bet that will be argued before the courts and may win as I think it's very fair in today's world to allow someone fair use to maintain their backup copies as formats change/obsolete over time.
But should you get fair use to protect you when you convert a DVD you purchased into a new copy of a Bluray? That seems like a different thing altogether, so not sure if that would be protected as a fair use exception to copyright.
afaik, a VHS recording is for time shifting purposes only. as in you should only have it for 24 hours or so. it doesn't mean you can permanently keep a copy. of course, that's what we all did back then.
fair use, again afaik, is more for satirical purposes no? as in showing a clip of a tv show/movie and commenting on it. schools have an out for this i think.