Hobby recognition of a variation for a long time has seemed to follow recognition in some catalog like SCD or Beckett. Now the PSA Registry is another source of "official recognition". People like Dick Gilkeson and others have put out lists they developed with many print oddities not recognized in the Catalogs. Sometimes they get recognized later , sometimes not. Some of them reach hobby recognition status anyway, like the 52 House Yellow Tiger
Print defects like the 58 Herrer and 57 Bakep got recognized in the years before ebay and all the internet scans of cards now available. Since that time print variants and defects have exploded . I tend to think that if you look hard enough and long enough you could find at least some minor print difference for almost every card , but certainly for many in each set
There is no one hobby recognized definition of a variation versus a recurring print defect that I know of. Some people, me included, think a variation is a card changed intentionally in the printing process by the manufacture. But even then there can be gray areas, for example cropping differences in DP cards. The 52 Mantle, Thompson and Robinson cards are examples. Probably not intended, but resulting from an intentional difference in the printing process for the card.
The 52 House is an interesting example. It could be viewed as a recurring print defect, but many think it is a true variation resulting from a change to the card in the printing process. So far it has not found catalog or Registry recognition, but I think most of us collectors of the 52 set believe it should be ( more than one variation actually...gray back/ different tongue)
There are a lot of variant collectors on here and I am sure they will chime in. I do not think there is a right or wrong answer for an individual collector in terms of his/her own collection. But what causes a card's value to take off is hobby recognition via a catalog or the Registry, because then master set collectors have to have it, whether it is a "true variation" or a recurring print defect. The House variant currently sells at a pretty good premium, but if it does make the Registry or Beckett or SCD, it's value will likely soar.. The 61 Fairly is a good example of how that can happen
I know people who have successfully lobbied Bartsch at SCD to list certain cards as variation. Persistence and hobby recognition in some form apparently helps. Beckett may have a similar process. I think the Registry seems to follow what the catalogs do eventually.
I collect both variations and recurring print differences to put with my sets. If some of the print defects later get recognized as variations, the value would go up and I would not be chasing that card, like I had to do with the Fairly card after it has started to rise in value. But even if never recognized in the hobby, and most will not because of the proliferation of them in recent years, I still enjoy having them with my sets.
Short answer is I think it is impossible to make total sense out of what is and is not recognized as variation in the hobby today. But there are a bunch of us here who like chasing and sharing them anyway