Potato potato, I suppose. Ultimately what counts is the creators intent, and how it’s categorized on IMDB / TVDB.
In Scrub’s case, it’s interesting to know that season 8 was intended as the final season, and what became season 9 (basically without the key stars) was to be a new show. ABC called it season 9, so it’s canonically season 9. Now it’s been stated that the new show is, if anything, a continuation of season 8, not 9.
It can go both ways. On one hand, you've got Roseanne, Mad About You, Murphy Brown. On the other, Fuller House, Saved By The Bell, Scrubs (2026). I'm sure part of which way it falls is dependent on contracts and which networks are involved.