It feels to me like if you have to specify which printing of a book to use because the amount of substantive errata is no longer able to be sifted through easily, then it's effectively a new edition.
If going from 7th to 8th edition of Intro Stats brings a few rewritten paragraphs, a two page new subject, and a handful of new homework problems, then I feel bad having the students buy it over a used copy of the old one even if the publisher wants to act like it's not just a cash grab in their part. If half the homework problems are different, it changed the software examples, altered which test for proportions it had, updated half of the examples, and added two new chapters then it kind of feels like a new thing and I'll recommend they get the new one.
The big genealogy book I have about Cappeln came with a page of edits tucked in. Since then I was emailed three more new pages. At some point there will be enough pages of new info that it will be awkward and painful to use the original printed book. It won't matter if the author wants to act like it's the same thing. It's kind of like the year book supplements that used to come out for encyclopedias - at some point you really just wanted a new set.
My son loves Minecraft, but hates how some of his books become outdated because there's a new Minecraft version out because the options and code don't exist anymore in the current versions. That the code and options in the book are obsolete doesn't change based on whether or not the author specified a version number in the book. If Minecraft stopped using version numbers it wouldn't change whether the books were obsolete. On the other hand some books don't have much at all that has changed and they work just fine with the new edition.
As has been noted elsewhere, plenty of tables used to play OD&D, B/X, and 1e at the same table. Others argued over whether 4e and essentials were different games. The only thing that seems abundantly clear to me is that what the publisher calls it is far from the biggest determinant into what the practicalities are.